Statistics Questions

In an article about health care coverage it was claimed that 25 of residents of Texas do not have health care coverage In a random sample of 260 residents of Texas it was found that 61 were uninsured Is this sufficient evidence to reject the claim of 25 uninsured Use a level of significance of 0 05 a State the appropriate null and alternative hypotheses Ho p 0 25 Select Ha p b Test your hypotheses and make and justify a statistical decision using the significance level of 5 Test statistic value rounded to 3 decimal places Select 0 25 p value rounded to 3 decimal places Select decision Select c Interpret your decision in the context of the problem Select Conclusion There Texas do not have health care coverage evidence to Select the claim that 25 of residents of

Regarding the previous question If it were later determined that it was important to be more than 95 confident and a new survey was commissioned how would that affect the minimum number you would need to survey Why

The following data are the ages of randomly selected patients in hospital intensive care units 4 38 64 35 67 42 29 68 62 74 58 Construct a 90 confidence interval to estimate of the mean age of the population of ICU patients Lower bound of 90 Confidence Interval round to nearest whole number Upper bound of 90 Confidence Interval round to nearest whole number years old years old

Two researchers Beth and Frank ask a random sample of teenagers whether or not they had been to the movies in the last month They find that their sample proportion p of teens who said yes was 8 80 When they construct a confidence interval based on this sample proportion Beth comes up with 73 87 while Frank gets 75 89 Indicate which interval has to be wrong and explain your choice

1 What is the difference between probability and odds Give an example of each 4 pts

If you wanted to decrease the width of your confidence interval would you increase or decrease your confidence level O increase decrease neither changing the confidence level does not change the width of a confidence interval

Part 2 of 5 Find the critical value Round the answer to at least two decimal places The critical value is 2 4403 Part 2 5 Part 3 of 5 Compute the test statistic Round the answer to at least two decimal places F X

Ho 0 0 H 0 0 This hypothesis test is a left tailed test Part 1 5 Part 2 of 5 Find the critical value Round the answer to at least two decimal places The critical value is X 5

and the critical value Round the answer to two decimal places The critical value fo 01 is 10 97 Compute the test statistic Round the answer to two decimal places F 8 35 Part 3 5 Determine whether to reject Ho Choose one the null hypothesis Ho X S

H 0 This hypothesis test is a left tailed Find the critical value Round the answer to two decimal places The critical value is 2 849 Part 2 5 test Compute the test statistic Round the answer to two decimal places F

There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store Thus the regression line is useful Round to two decimal places d 7 e Interpret There is a 77 chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store Given any group that spends a fixed amount of time at the store 77 of all of those customers will spend the predicted amount of money at the store 77 of all customers will spend the average amount of money at the store O There is a large variation in the amount of money that customers spend at the store but if you only look at customers who spend a fixed amount of time at the store this variation on average is reduced by 77 f The equation of the linear regression line is y Please show your answers to two decimal places g Use the model to predict the amount of money spent by a customer who spends 14 minutes at the store Dollars spent Please round your answer to the nearest whole number h Interpret the slope of the regression line in the context of the question For every additional minute customers spend at the store they tend to spend on averge 4 04 more money at the store O The slope has no practical meaning since you cannot predict what any individual customer will spend As x goes up y goes up i Interpret the y intercept in the context of the question If a customer spends no time at the store then that customer will spend 6 51 The y intercept has no practical meaning for this study O The best prediction for a customer who doesn t spend any time at the store is that the customer will spend 6 51 The average amount of money spent is predicted to be 6 51

Part 2 of 5 Find the critical value Round the answer to two decimal places The critical value f0 05 is 3 18 Part 2 5 Part 3 of 5 Compute the test statistic Round the answer to two decimal places F X 5

in anticipation of an upcoming election officials in Rising Falls County are looking at the distance from each voter s home to that voter s nearest polling station Assume that the population of all such distances for voters in Rising Falls County is approximately normally distributed An article for the newspaper Keeping It Political claimed that the mean of this population is 6 45 km You want to test this claim so you select a random sample of 22 Rising Falls County voters and for each you record the distance the voter lives from their nearest polling station Follow the steps below to construct a 90 confidence interval for the population mean of all the distances voters in Rising Falls County live from their nearest polling station Then state whether the confidence interval you construct contradicts the reporter s claim If necessary consult a list of formulas a Click on Take Sample to see the results for your random sample Take Sample Sample size 0 Point estimate 0 Sample standard deviation Critical value Compute Enter the values of the sample size the point estimate of the mean the sample standard deviation and the critical value you need for your 90 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute 0 000 Number of people 0 000 22 2 000 Sample mean 4 795 Standard error 4 000 Margin of error 90 confidence interval b Based on your sample graph the 90 confidence interval for the population mean of all the distances the voters in Rising Falls County live from their nearest polling station Enter the values for the lower and upper limits on the graph to show your confidence interval For the point enter the claim 6 45 from the article 90 confidence interval 5 000 6 000 Sample standard deviation 2 312 O No the confidence interval does not contradict the claim The mean of 6 45 km from the article is inside the 90 confidence interval O No the confidence interval does not contradict the claim The mean of 6 45 km from the article is outside the 90 confidence interval O Yes the confidence interval contradicts the claim The mean of 6 45 km from the article is inside the 90 confidence interval O Yes the confidence interval contradicts the claim x Critical values 10 005 2 831 10 010 2 518 10 025 2 080 10 050 1 721 10 100 1 323 8 000 X c Does the 90 confidence interval you constructed contradict the claim made in the article Choose the best answer from the choices below 10 000 10 000 S EE A M

A grocery store manager did a study to look at the relationship between the amount of time in minutes customers spend in the store and the amount of money in dollars they spend The results of the survey are shown below Time Money 122 72 64 30 22 20 30 30 22 122 104 81 a Find the correlation coefficient r b The null and alternative hypotheses for correlation are Ho 0 H HB 0 The p value is 19 88 Round to four decimal places c Use a level of significance of a 0 05 to state the conclusion of the hypothesis test in the context of the study Round to 2 decimal places There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store O There is statistically insignificant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store Thus the use of the regression line is not appropriate There is statistically significant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store d 7 e Interpret There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store Thus the regression line is useful Round to two decimal places There is a 77 chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store f The equation of the linear regression line is Given any group that spends a fixed amount of time at the store 77 of all of those customers will spend the predicted amount of money at the store 77 of all customers will spend the average amount of money at the store O There is a large variation in the amount of money that customers spend at the store but if you only look at customers who spend a fixed amount of time at the store this variation on average is reduced by 77 Please show your answers to two decimal places

s the proportion of wildfires caused by humans in the south higher than the proportion of wildfires caused by humans in the west 381 of the 514 randomly selected wildfires looked at in the south were caused by humans while 368 of the 531 randomly selected wildfires looked at the west were caused by humans What can be concluded at the 0 01 level of significance a For this study we should use Select an answer b The null and alternative hypotheses would be Select an answer Ho H Select an answer Select an answer Select an answer c The test statistic d The p value e The p value is Q f Based on this we should g Thus the final conclusion is that Select an answer Select an answer please enter a decimal Please enter a decimal please show your answer to 3 decimal places Please show your answer to 4 decimal places Select an answer the null hypothesis 0 The results are statistically insignificant at a 0 01 so there is statistically significant evidence to conclude that the population proportion of wildfires caused by humans in the south is equal to the population proportion of wildfires caused by humans in the west The results are statistically insignificant at a 0 01 so there is insufficient evidence to conclude that the population proportion of wildfires caused by humans in the south is higher than the population proportion of wildfires caused by humans in the west The results are statistically significant at a 0 01 so there is sufficient evidence to conclude that the proportion of the 514 wildfires that were caused by humans in the south is higher than the proportion of the 531 wildfires that were caused by humans in the west The results are statistically significant at a 0 01 so there is sufficient evidence to conclude that the population proportion of wildfires caused by humans in the south is higher than the population proportion of wildfires caused by humans in the west

Is the average time to complete an obstacle course longer when a patch is placed over the right eye than when a patch is placed over the left eye Thirteen randomly selected volunteers first completed an obstacle course with a patch over one eye and then completed an equally difficult obstacle course with a patch over the other eye The completion times are shown below Left means the patch was placed over the left eye and Right means the patch was placed over the right eye Time to Complete the Course Right 43 45 41 48 42 44 42 50 Left 45 46 41 46 44 44 42 53 Assume a Normal distribution What can be concluded at the the a 0 01 level of significance level of significance For this study we should use Select an answer a The null and alternative hypotheses would be Ho Select an answer H Select an answer Select an answer Select an answer b The test statistic c The p value d The p value is 8 a e Based on this we should f Thus the final conclusion is that Select an answer Select an answer please enter a decimal Please enter a decimal please show your answer to 3 decimal places Please show your answer to 4 decimal places 8 Select an answer the null hypothesis The results are statistically significant at a 0 01 so there is sufficient evidence to conclude that the eight volunteers that were completed the course slower on average with the patch over the right eye compared to the left eye The results are statistically insignificant at a 0 01 so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is greater than the population mean time to complete the obstacle course with a patch over the left eye The results are statistically insignificant at a 0 01 so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye The results are statistically significant at a 0 01 so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is greater than the population mean time to complete the obstacle course with a patch over the left eye

x c g o o d for letter in x message letter Consider the above code How many times will the loop iterat 08 07

The average American gets a haircut every 37 days Is the average different for college students The data below shows the results of a survey of 11 college students asking them how many days elapse between haircuts Assume that the distribution of the population is normal 30 41 29 24 34 38 32 28 34 25 34 What can be concluded at the the x 0 05 level of significance level of significance a For this study we should use Select an answer b The null and alternative hypotheses would be Ho Select an answer H Select an answer c The test statistic d The p value e The p value is a f Based on this we should Select an answer the null hypothesis g Thus the final conclusion is that please show your answer to 3 decimal places Please show your answer to 3 decimal places The data suggest the population mean is not significantly different from 37 at x 0 05 so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is equal to 37 The data suggest the populaton mean is significantly different from 37 at a 0 05 so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is different from 37 The data suggest the population mean number of days between haircuts for college students is not significantly different from 37 at a 0 05 so there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is different from 37

Do political science classes require less writing than history classes The 50 randomly selected political science classes assigned an average of 16 3 pages of essay writing for the course The standard deviation for these 50 classes was 5 6 pages The 42 randomly selected history classes assigned an average of 19 pages of essay writing for the course The standard deviation for these 42 classes was 3 2 pages What can be concluded at the a 0 01 level of significance For this study we should use Select an answer a The null and alternative hypotheses would be Ho Select an answer H Select an answer Select an answer Select an answer Select an answer Select an answer b The test statistic c The p value d The p value is a e Based on this we should Select an answer the null hypothesis f Thus the final conclusion is that please show your answer to 3 decimal places Please show your answer to 4 decimal places 8 The results are statistically insignificant at a 0 01 so there is insufficient evidence to conclude that the population mean number of pages of writing that political science classes require is less than the population mean number of pages of writing that history classes require The results are statistically significant at a 0 01 so there is sufficient evidence to conclude that the mean number of required pages for the 50 political science classes that were observed is less than the mean number of required pages for the 42 history classes that were observed The results are statistically significant at a 0 01 so there is sufficient evidence to conclude that the population mean number of pages of writing that political science classes require is less than the population mean number of pages of writing that history classes require The results are statistically insignificant at a 0 01 so there is statistically significant evidence to conclude that the population mean number of pages of writing that political science classes require is equal to the population mean number of pages of writing that history classes require

Error in if condition missing value where TRUE FALSE needed Consider the above message Which of the following could be the value of condition inside the if statement Note this assumes you have R version 4 2 0 as per the syllabus O NaN O NA NA O NA

What happens when the condition passed to an if statement is vector with length not equal to 1 Note this assumes you have R version 4 2 0 as per the syllabus O An error occurs The code executes with neither warning nor error O It depends on the condition in the if statement A warning occurs

Are if statements required to be followed by else statements It depends on the condition in the if statement No O Yes

For all responses do not use a dollar sign or a percent sign in your responses numbers 2 4 1 In a survey of 1000 U S teenagers 45 consider entrepreneurship as a career option The margin of error is 13 296 a Give an interval that is likely to contain the exact percent of U S teenagers who consider entrepreneurship as a career option Between 45 2 and 41 5 b The population of teenagers in the U S is about 21 25 million Estimate the number of teenagers in the U S who consider entrepreneurship as a career option Between 10 24 million and 8 88 million round to the nearest 100th C

elderly patients On her new doctor s website it says that the mean systolic blood pressure among elderly females is 120 millimeters of mercury mmHg Donna believes the value is actually higher She bases her belief on a recently reported study of 10 randomly selected elderly females The sample mean systolic blood pressure was 139 mmHg and the sample standard deviation was 25 mmHg Assume that the systolic blood pressures of elderly females are approximately normally distributed Based on the study at the 0 05 level of significance can it be concluded that the population mean systolic blood pressure among elderly females is greater than 120 mmHg Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H H O H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the critical value Round to three or more decimal places e Can it be concluded that the mean systolic blood pressure among elderly females is greater than 120 mmHg OYes O No H XI 0 0 0 0 X O S OSO 0 0 P P 020 0 0

Can you conclude that the standard deviation of the breaking strength Composite 2 is greater Use the a 0 05 level of significance State the null and alternate hypotheses Ho 0 0 H 0 This hypothesis test is a left tailed Part 1 5 Find the critical value Round the answer to two decimal places The critical value is test X Send data to Excel 3

while being treated with a particular nutrient is 36 centimeters To check whether this is still accurate heights are measured for a random sample of 14 Begonias grown while being treated with the nutrient The sample mean and sample standard deviation of those height measurements are 33 centimeters and 8 centimeters respectively Assume that the heights of treated Begonias are approximately normally distributed Based on the sample can it be concluded that the population mean height of treated begonias u is different from that reported in the journal Use the 0 10 level of significance Perform a two tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H 0 Ho H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the p value Round to three or more decimal places e Can it be concluded that the mean height of treated Begonias is different from that reported in the journal OYes No x X O P S Q 0 0 OSO 020 0 0 0 0

Find the critical values fo 025 and fo 10 for f3 17 The critical value f0 025 for f3 17 is 4 01116 The critical value fo 10 for f3 17 is 2 43743 Part 1 2 Part 2 of 2 Do you reject H at the a 0 025 and the a 0 10 level We Choose one Ho at the a 0 025 level Ho at the a 0 10 level We Choose one X 3

State the null and alternate hypothesis Ho 0 0 H 0 0 This is a right tailed Part 1 5 Part 2 of 5 test Find the critical value Round the answer to two decimal places The critical value fo 05 is X

H 0 0 This is a two tailed Correct Answer Ho 0 0 H 0 0 This is a right tailed test Part 1 5 test Find the critical value Round the answer to two decimal places The critical value f0 01 is 15

An electronics manufacturing process has historically had a mean completion time of 75 minutes It is claimed that due to improvements in the process the mean completion time is now less than 75 minutes A random sample of 14 completion times using the new process is taken The sample has a mean completion time of 72 minutes with a standard deviation of 9 minutes Assume that completion times using the new process are approximately normally distributed At the 0 05 level of significance can it be concluded that the population mean completion time using the new process is less than 75 minutes Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H H 0 H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places 0 d Find the p value Round to three or more decimal places e Can it be concluded that the mean completion time using the new process is less than 75 minutes Yer No x X 0 0 X O S 2 OSO O O P Q G 010 020 0 0

An F test with 3 degrees of freedom in the numerator and 17 degrees of freedom in the denominator produced a test statistic whose value was 3 13 The null and alternate hypotheses were Ho 0 0 versus H 0 02 Part 0 2 Part 1 of 2 Find the critical values fo 025 and fo 10 for f3 17 The critical value fo 025 for f3 17 is The critical value fo 10 for f3 17 is X

Can you conclude that the standard deviation of IQ is greater for the secondborn than the firstborn Let o denote the standard deviation in the IQs of firstborn sons Use the a 0 10 level Part 0 5 Part 1 of 5 State the null and alternate hypotheses Ho Choose one 0 H 0 Choose one 0 Send data to Excel This hypothesis test is a Choose one test 8 E B ola

Hockey sticks The breaking strength of hockey stick shafts made of two different graphite kevlar composites yields the following results in Newtons Composite 1 549 1 527 9 525 4 530 9 553 8 506 8 490 1 538 571 580 7 594 6 567 8 567 2 548 1 584 6 535 8 535 2 561 552 9 579 3 553 578 1 Part 0 5 5 State the null and alternate hypotheses Ho H Composite 2 Can you conclude that the standard deviation of the breaking strength Composite 2 is greater Use the a 0 05 level of significance 6 0 0 Send data to Excel 0 0 0 Co E V d

Sugar content A broth used to manufacture a pharmeceutical product has its sugar content in milligrams per milliliter measured several times on each of three successive days Can you conclude that the variability of the process is greater on the second day than on the third day Let o denote the variability of sugar content on the second day and 62 denote the variability of sugar content on the third day Use the a 0 05 level and the critical value method with the table Day 1 Day 2 Day 3 Send data to Excel Part 0 5 Part 1 of 5 5 0 4 8 5 1 4 8 5 1 4 8 4 8 5 0 5 2 4 9 5 8 4 7 4 7 5 1 4 9 5 4 5 3 5 3 4 8 5 7 6 0 5 3 6 3 4 7 5 1 5 1 5 9 4 7 4 9 5 7 State the null and alternate hypothesis Ho H O O 01 0 0 02

Frozen computer A computer system administrator noticed that computers running a particular operating system seem to freeze up more often as the installation of the operating system ages She measures the time in minutes before freeze up for 6 computers one month after installation and for 6 computers seven months after installation The results are shown Can you conclude that the time to freeze up is less variable in the seventh month than the first month after installation Let o denote the variability in time to freeze up in the first month after installation Use the a 0 01 level and the critical value method with the table Part 0 5 State the null and alternate hypothesis Ho H One month Seven months 0 0 0 0 0 0 245 3 207 4 233 1 215 9 235 1 225 6 149 4 156 4 103 3 84 3 53 2 127 3 Send data to Excel Espanol 00 E E ola

H 2 The critical value fo 025 for F5 12 is Find the critical value fo 025 for FS 12 Round your answer to two decimal places D X

Use the Empirical Rule to answer the questions below The distribution of weights for newborn babies is approximately normally distributed with a mean of 7 6 pounds and a standard deviation of 0 8 pounds 1 What percent of newborn babies weigh more than 8 4 pounds 2 The middle 95 of newborn babies weigh between pounds 3 What percent of newborn babies weigh less than 6 pounds and 4 Approximately 50 of newborn babies weigh more than 5 What percent of newborn babies weigh between 6 8 and 10 pounds 196 pounds

Use the given data to find the equation of the regression line Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line x 11 10 4 7 3 12 6 5 13 9 8 D y 19 78 19 16 8 04 15 20 4 94 20 04 13 16 10 78 19 94 18 20 16 88 y 3 10 1 5 x Round to two decimal places as needed Create a scatterplot of the data Choose the correct graph below OA Ay 25 20 15 10 5 0 0 5 10 15 20 25 Q Q OB 25 20 Ay 15 109 5 0 0 5 10 15 20 25 Q Q Identify a characteristic of the data that is ignored by the regression line OA There is no trend in the data OB There is an influential point that strongly affects the graph of the regression line OC The data has a pattern that is not a straight line OD There is no characteristic of the data that is ignored by the regression line SEER C 25 20 153 10 ag 53 0 0 5 10 15 20 25 OU O D Ay 25 m 20 15 10 5 0 0 5 10 15 20 25

Many say that baseball is a game with low success rate Consider Mookie Betts one of the greatest players the sport has ever seen He had a batting average BA of 346 during the 2018 season His batting average was the highest of all players for that year A player s batting average is computed by dividing the number of times a player has a hit by the player s total number of at bats BA Number of Hits Number of At Bats Notice that this formula looks a lot like a probability where the sample space is the set of all at bats and the event is getting a hit When fans talk about batting averages they commonly think of it in terms of probability That is if a player is batting 250 then there is a 25 chance that they will be a hit at their next at bat 1 Do you agree with the interpretation of the batting average as a probability Is it possible to compute the theoretical probability that a player will get a hit when at bat Explain you answer 2 Let s return our attention to Mookie Betts Betts had 520 at bats during the 2018 season how many hits did he have that season Round your answer to the nearest whole number 3 Suppose that Mookie Betts had another 20 at bats during the 2018 season Assume he had a BA of 500 for those 20 at bats What would his new batting average be with these extra 20 at bats

Determine whether to reject Ho Do not reject the null hypothesis Ho Part 4 5 Part 5 of 5 State a conclusion There Choose one enough evidence to conclude that the population standard deviation o is less than 68 is is not X

Find the critical value Round the answer to three decimal places For a 0 01 the critical value is 57 3421 Correct Answer 57 342 Part 2 5 Part 3 of 5 Compute the test statistic Round the answer to three decimal places

The price of an item has been reduced by 55 The originat price was 37

H 0 This hypothesis test is a two tailed Part 2 of 5 18 Part 2 5 Find the critical values Round the answers to three decimal places For a 0 01 the critical values are 9 886 and 45 559 Part 3 of 5 test Compute the test statistic Round the answer to three decimal places

Part 3 of 5 Compute the test statistic Round the answer to three decimal places as needed x 17 594 Part 3 5 Part 4 of 5 Determine whether to reject Ho Choose one the null hypothesis Ho Reject X 3

Determine whether to reject Ho At the a 0 05 level reject Part 4 5 Part 5 of 5 State a conclusion the null hypothesis Ho There Choose one enough evidence to conclude that the population standard deviation of the weights of one year old

Find the linear and quadratic functions that best fit the data points 0 5 6 1 5 3 2 5 0 3 4 9 and 4 5 1 Which of the two functions best fits the data The linear function that best fits the data points is y Type an expression using x as the variable Use integers or decimals for any numbers in the expression Round to two decimal places as needed

The hypotheses are provided above This hypothesis test is a left tailed Part 2 of 5 Find the critical value Critical value 4 5748 Part 2 5 Part 3 of 5 test Compute the test statistic Round the answer to three decimal places as needed

A random sample of size 12 from a normal distribution has standard deviation s 86 Test Ho o 68 versus H 0 68 Use the a 0 05 level of significance Part 1 of 5 The hypotheses are provided above This hypothesis test is a left tailed Part 1 5 Part 2 of 5 Find the critical value pt 1 of 3 Critical value test

H 0 This hypothesis test is a right tailed Part 2 of 5 3 Part 2 5 Find the critical value Round the answer to three decimal places For a 0 05 the critical value is 36 415 Part 3 of 5 test statictic Round the answer to three decimal places

State the appropriate null and alternate hypotheses Ho o 3 H 0 This hypothesis test is a right tailed Part 1 5 Part 2 of 5 3 test Find the critical value Round the answer to three decimal places For g 0 05 the critical value in