Statistics Questions

An event A will occur with probability 0 5 An event B will occur with probability 0 6 The probability that both A and B will occur is 0 1 The conditional probability of B given A is OA 5 6 OB 1 5 O C 1 6 O D The answer cannot be determined from the information given

Suppose we toss a coin and roll a die Let A be the event that the number of spots showing on the die is three or less and B be the event that the coin comes up heads The events A and B are O A reciprocals O B independent O C conditional O D disjoint

According to M Ms Web site each package of the milk chocolate candies typically contain 14 brown 13 red 14 yellow 16 green 24 blue and 20 orange M Ms You go to the store and buy a standard sized package When you open it you find that it contains 51 M Ms distributed as follows Color Brown Blue Red 4 Yellow 10 Frequency 8 11 The variable color is O A discrete O B continuous C quantitative OD None of the answer choices is correct Green 4 Orange 11

1 A 10 point midterm test results in grades that are normally distributed with a mean of 7 5 and a standard deviation of 8 The professor plans to give 10 of the class A s 30 B s 40 C s 15 D s and 5 F s What are the minimum and maximum test scores for each grade

Find the appropriate p value to test the null hypothesis Ho P1 P2 using a significance level of 0 05 n 100 n 0 0021 140 x 41 x 35 X1

Given the linear correlation coefficient r and the sample size n determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation Use a significance level of 0 05 r 0 863 n 5 O Critical values r 0 950 significant linear correlation O Critical values r 0 878 significant linear correlation Critical values r 0 878 no significant linear correlation

Compute the test statistic used to test the null hypothesis that p P2 In a vote on the Clean Water bill 41 of the 205 Democrats voted for the bill while 42 of the 230 Republicans voted for it O 0 127 O 0 211 O 0 732

Construct the indicated confidence interval for the difference between population proportions P P2 Assume that the samples are independent and that they have been randomly selected In a random sample of 500 people aged 20 24 22 were smokers In a random sample of 450 people aged 25 29 14 were smokers Construct a 95 confidence interval for the difference between the population proportions p P 0 035 P1 P2 0 125 O 0 048 P1 P2 0 112

Construct the indicated confidence interval for the difference between the two population means Assume that the two samples are independent and that they have been randomly selected Two types of flares are tested for their burning times in minutes and sample results are given below Brand X n 35 x bar 19 4 s 1 4 Brand Y n 40 x bar 15 1 s 0 8 Construct a 95 confidence interval for the differences x y based on the sample data 3 8 x Hy 4 8 Q 3 5 Hx y 5 1

Find the value of the linear correlation coefficient r The paired data below consist of the costs of advertising in thousands of dollars and the number of products sold in thousands Cost Number O 0 246 O 0 708 0 071 9 2 3 4 2 5 9 10 85 52 55 68 67 86 83 73

From the sample statistics find the value of p bar used to test the hypothesis that the population proportions are equal n 541 n 1927 x 160 x 689 O 0 344

Use the given data to find the equation of the regression line Round the final values to three significant digits if necessary X 1 3 5 7 9 y v 143 116 100 98 90 O y 140 4 6 2x O y 150 7 6 8x O y 150 7 6 8x

Find the best predicted value of y corresponding to the given value of x Ten pairs of data yield r 0 003 the regression equation 2 3x and y bar 5 What is the best predicted value of y for x 2 O 8 0 O 17 0 O 7 0

OT y x 1 y x 4 solution x y

Sy 1 x 2 TTTTTTT solution x y

X H 3x 3 TO solution x H y

I Solve and graph y 8x 10 9 8 7 100 la 937DDTANE B 6 5 4 3 2 10 14 51 789 7 8 10 2 3 4 5 6 7 8 9 10

8 9 10 2 Where is the y intercept f x 6 4 3 2 1 1 2 03 4 LO T

Assembly Product design Electricity Set up Total overhead allocated 4 Job 42 Assembly Product design Electricity set up Total our head allocated DLH EM MH Set ups DLM EH MH setups 360 42 50 5 650 48 60 7 42 prDLH 15120 56 per EH 2352 140 2 0 per MH 9 175 per setup 875 18 487 42 per DLH Date 5 6 pm EH 200 per LMH 175 per setup 27 300 2688 168 1225 31 381

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2 Sunn Company manufactures a single product that sells for 100 per unit and whose variable costs are 76 per unit The company s annual fixed costs are 338 400 ints eBook Hint Print References 1 Prepare a contribution margin income statement at the break even point 2 If the company s fixed costs increase by 126 000 what amount of sales in dollars is needed to break even Complete this question by entering your answers in the tabs below Required 1 Required 2 Prepare a contribution margin income statement at the break even point SUNN COMPANY Contribution Margin Income Statement at Break Even Amount Check m

Find the value of Za ZO 44 Round to two decimal places as nee

Determine the total area under the standard normal curve in parts a through c below a Find the area under the normal curve to the left of z 2 plus the area under the normal curve to the right of z 2 The combined area is Round to four decimal places as needed b Find the area under the normal curve to the left of z 1 54 plus the area under the normal curve to the right of z 2 54 The combined area is Round to four decimal places as needed c Find the area under the normal curve to the left of z 0 29 plus the area under the normal curve to the right of z 1 10 The combined area is Round to four decimal places as needed

Suppose the lengths of human pregnancies are normally distributed with 266 days and a 16 days Complete parts a and b below BOCCH a The figure to the right represents the normal curve with 266 days and a 16 days The area to the left of X 240 is 0 0521 Provide two interpretations of this area Provide one interpretation of the area using the given values Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals A The proportion of human pregnancies that last less than OB The proportion of human pregnancies that last more than days is days is OB The proportion of human pregnancies that last less than days is Provide a second interpretation of the area using the given values Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals OA The probability that a randomly selected human pregnancy lasts less than OB The probability that a randomly selected human pregnancy lasts more than b The figure to the right represents the normal curve with 266 days and 16 days The area between x 285 and x 305 is 0 1101 Provide two interpretations of this area Provide one interpretation of the area using the given values Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals Use ascending order OA The proportion of human pregnancies that last between and days is 240 266 or more than days is days is ON A 266 285 305 or more than Provide a second interpretation of the area using the given values Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals Use ascending order OA The probability that a randomly selected human pregnancy lasts less than OB The probability that a randomly selected human pregnancy lasts between and days is ON days is

The random number generator on calculators randomly generates a number between 0 and 1 The random variable X the number generated follows a uniform probability distribution a Identify the graph of the uniform density function b What is the probability of generating a number between 0 09 and 0 98 c What is the probability of generating a number greater than 0 83 a Choose the correct graph of the uniform density function below O A OB 1 2 1 0 8 0 6 0 4 0 2 Density 04 0 0 2 0 4 0 6 0 8 1 b The probability is The probability is X 1 2 Q 1 2 1 0 8 0 6 0 4 0 2 Density 0 0 0 2 0 4 0 6 0 8 1 Simplify your answer Simplify your answer X 1 2 2 C 1 2 1 0 8 0 6 0 4 0 2 Density 0 0 0 2 0 4 0 6 0 8 1 2

A study was conducted that resulted in the following relative frequency histogram Determine whether or not the histogram indicates that a normal0 4 distribution could be used as a model for the variable 0 2 1000 2000 3000 4000 5000 Choose the correct answer below OA The histogram is bell shaped so a normal distribution could not be used as a model for the variable OB The histogram is bell shaped so a normal distribution could be used as a model for the variable OC The histogram is not bell shaped so a normal distribution could be used as a model for the variable The histogram is not bell shaped so a normal distribution could not be used as a model for the variable

A simple random sample of 10 pages from a dictionary is obtained The numbers of words defined on those pages are found with the results n 10 x 55 4 words s 16 2 words Given that this dictionary has 1436 pages with defined words the claim that there are more than 70 000 defined words is equivalent to the claim that the mean number of words per page is greater than 48 7 words Us a 0 01 significance level to test the claim that the mean number of words per page is greater than 48 7 words What does the result suggest about the claim that there are more than 70 000 defined words Identify the null and alternative hypotheses test statistic P value and state the final conclusion that addresses the original claim Assume that the population is normally distributed What are the null and alternative hypotheses O A Ho H 48 7 words H 48 7 words C Ho H 48 7 words H 48 7 words Determine the test statistic Round to two decimal places as needed Determine the P value Round to three decimal places as needed State the final conclusion that addresses the original claim Ho There is evidence to support the claim that there CID OB Ho 48 7 words H 48 7 words O D Ho H 48 7 words H H 48 7 words 70 000 defined words in the dictionary

A random sample of 834 births included 433 boys Use a 0 01 significance level to test the claim that 51 4 of newborn babies are boys Do the results support the belief that 51 4 of newborn b are boys H p 0 514 OC Ho p 0 514 H p 0 514 OD Ho p 0 514 H p0 514 Identify the test statistic for this hypothesis test The test statistic for this hypothesis test is 0 23 Round to two decimal places as needed Identify the P value for this hypothesis test The P value for this hypothesis test is 0 411 Round to three decimal places as needed Identify the conclusion for this hypothesis test O A Reject Ho There is sufficient evidence to warrant rejection of the claim that 51 4 of newborn babies are boys OB Reject Ho There is not sufficient evidence to warrant rejection of the claim that 51 4 of newborn babies are boys OC Fail to reject Ho There is sufficient evidence to warrant rejection of the claim that 51 4 of newborn babies are boys O D Fail to reject Ho There is not sufficient evidence to warrant rejection of the claim that 51 4 of newborn babies are boys Do the results support the belief that 51 4 of newborn babies are boys OA The results support the belief that 51 4 of newborn babies are boys because there was sufficient evidence to show that the belief is true OB The results do not support the belief that 51 4 of newborn babies are boys because there was sufficient evidence to show that the belief is untrue OC The results support the belief that 51 4 of newborn babies are boys because there was no evidence to show that the belief is untrue

Use the sample data and confidence level given below to complete parts a through d A drug is used to help prevent blood clots in certain patients In clinical trials among 4376 patients treated with the drug 139 developed the adverse reaction of nausea Construct a 95 confidence interval for the proportion of adverse reactions a Find the best point estimate of the population proportion p 0 032 Round to three decimal places as needed b Identify the value of the margin of error E E Round to three decimal places as needed c Construct the confidence interval p 0 Round to three decimal places as needed d Write a statement that correctly interprets the confidence interval Choose the correct answer below OA One has 95 confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion OB One has 95 confidence that the sample proportion is equal to the population proportion OC 95 of sample proportions will fall between the lower bound and the upper bound OD There is a 95 chance that the true value of the population proportion will fall hebwoon tha

You randomly select one card from a 52 card deck Find the probability of selecting black ten or a black queen 13 26 12 13 01 12

A genetic experiment with peas resulted in one sample of offspring that consisted of 449 green peas and 160 yellow peas a Construct a 90 confidence interval to estimate of the percentage of yellow peas b Based on the confidence interval do the results of the experiment appear to contradict the expectation that 25 of the offspring peas would be yellow a Construct a 90 confidence interval Express the percentages in decimal form p Round to three decimal places as needed b Based on the confidence interval do the results of the experiment appear to contradict the expectation that 25 of the offspring peas would be yellow O No the confidence interval includes 0 25 so the true percentage could easily equal 25 OYes the confidence interval does not include 0 25 so the true percentage could not equal 25

Independents Suppose that two group members are randomly selected in succession to attend a political convention Find the probability of selecting an Independent and then a Democrat Probability of Compound Events Independent Events Dependent Events P A and B P A P B P A and B P A Mutually Exclusive Events Not Mutually Exclusive Events P A or B P A P B P A or B P A 28 153 14 81 04 153

Use the sample data and confidence level given below to complete parts a through d A drug is used to help prevent blood clots in certain patients In clinical trials among 4376 patients treated with the drug 139 developed the adverse reaction of nausea Construct a 95 confidence interval for the proportion of adverse reactions a Find the best point estimate of the population proportion p Round to three decimal places as needed b Identify the value of the margin of error E E 0 Round to three decimal places as needed c Construct the confidence interval p Round to three decimal places as needed

Solve the problem For large numbers of degrees of freedom the critical x values can be 2 z 2k 1 where k is the number of degrees of freedom and z is the critical value To find the lower critical value the negative z value is used to find the upper critical value the positive z value is used Use this approximation to estimate the critical value of x in a two tailed hypothesis test with n 104 and 0 10 approximated using the formula x OA 80 300 and x 127 406 OB 285 903 and x 122 735 OC 81 186 and x 128 520 OD 84 992 and x 21 646

Use the Hypothesis Testing Identify Null and Alternative Hypotheses flow chart interactive to answer the following question Which of the following is not a valid expression for an alternative hypothesis H Choose the correct answer below OA p 0 5 OB 98 6 C p 1 4 OD 40

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects After treatment with the drug 14 subjects had a mean wake time of 97 2 min and a standard deviation of 42 3 min Assume that the 14 sample values appear to be from a normally distributed population and construct a 98 confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments Does the result indicate whether the treatment is effective Find the confidence interval estimate CO min o min Round to two decimal places as needed Does the result indicate whether the treatment is effective OA Yes the confidence interval indicates that the treatment is not effective because the interval does not contain 97 2 minutes OB Yes the confidence interval indicates that the treatment is not effective because the interval contains 0 minutes OC No the confidence interval does not indicate whether the treatment is effective OD Yes the confidence interval indicates that the treatment is not effective because the interval does not contain 0 minutes OE Yes the confidence interval indicates that the treatment is effective because the interval does not contain 0 minutes OF Yes the confidence interval indicates that the treatment is effective because the interval contains 0 minutes OG Yes the confidence interval indicates that the treatment is effective bonnung

Use the given information to find the p value Also use a 0 05 significance level and state the conclusion about the null hypothesis reject the null hypothesis or fail to reject the null hypothesis With H p 3 the test statistic is z 0 78 OA 0 2177 fail to reject the null hypothesis B 0 4354 fail to reject the null hypothesis OC 0 2177 reject the null hypothesis OD 0 4354 reject the null hypothesis

The director of research and development is testing a new medicine She wants to know if there is evidence at the 0 05 level that the medicine relieves pain in more than 380 seconds For a sample of 18 patients the mean time in which the medicine relieved pain was 386 seconds with a standard deviation of 20 Assume the population distribution is approximately normal Step 1 of 3 State the null and alternative hypotheses Answer Ho Tables Keypad Keyboard Shortcuts

A simple random sample of 10 pages from a dictionary is obtained The numbers of words defined on those pages are found with the results n 10 x 55 4 words s 16 2 words Given that this dictionary has 1436 pages with defined words the claim that there are more than 70 000 defined words is equivalent to the claim that the mean number of words per page is greater than 48 7 words Use a 0 01 significance level to test the claim that the mean number of words per page is greater than 48 7 words What does the result suggest about the claim that there are more than 70 000 defined words Identify the null and alternative hypotheses test statistic P value and state the final conclusion that addresses the original claim Assume that the population is normally distributed What are the null and alternative hypotheses OA Ho H 48 7 words H 48 7 words OC Ho H 48 7 words H 48 7 words Determine the test statistic Round to two decimal places as needed Determine the P value Round to three decimal places as needed State the final conclusion that addresses the original claim Ho There is OB Ho 48 7 words H 48 7 words O D Ho H 48 7 words H H 48 7 words evidence to support the claim that there 70 000 defined words in the dictionary

A data set about speed dating includes like ratings of male dates made by the female dates The summary statistics are n 190 x 5 81 s 2 27 Use a 0 05 significance level to test the claim that the population mean of such ratings is less than 6 00 Assume that a simple random sample has been selected Identify the null and alternative hypotheses test statistic P value and state the final conclusion that addresses the original claim What are the null and alternative hypotheses OA Ho 6 00 H 6 00 OC Ho 6 00 H 6 00 Determine the test statistic Round to two decimal places as needed Ho There is Determine the P value Round to three decimal places as needed State the final conclusion that addresses the original claim population of ratings is OB Ho H 6 00 H 6 00 6 00 O D Ho 6 00 H 6 00 evidence to conclude that the mean of the

A formal hypothesis test is to be conducted using the claim that the mean body temperature is equal to 98 6 F What is the null hypothesis and how is it denoted OA Ho 98 6 F OB Ho p 98 6 F OC Ho H 98 6 F O D Ho p 98 6 F

In a study of cell phone usage and brain hemispheric dominance an Internet survey was e mailed to 6988 subjects randomly selected from an online group involved with ears There were 1339 surveys returned Use a 0 01 significance level to test the claim that the return rate is less than 20 Use the P value method and use the normal distribution as an approximation to the binomial distribution Identify the null hypothesis and alternative hypothesis OA Ho p 0 2 H p 0 2 OC Ho p 0 2 H p 0 2 O E Ho p 0 2 H p 0 2 0 Round to two decimal places as needed The test statistic is z The P value is Round to three decimal places as needed Because the P value is There is OB B Ho p 0 2 H p 0 2 O D Ho p0 2 H p 0 2 OF Ho p 0 2 H p 0 2 the significance level the null hypothesis evidence to support the claim that the return rate is less than 20

Assume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors Use the table below to find the minimum sample size needed to be 99 confident that the sample standard deviation s is within 1 of o Is this sample size practical 6 To be 95 confident that s is within of the value of o the sample size In should be at least To be 99 confident that s is within of the value of o the sample size In should be at least The minimum sample size needed is Is this sample size practical 1 5 10 20 30 40 50 OC Yes because 19 205 768 192 48 21 12 8 1 5 10 20 30 40 50 33 218 1 336 336 85 38 22 14 OA Yes because the sample size should be as large as possible for most applications OB No because the sample size is excessively large to be practical for most applications the sample size is small enough to be practical for most applications O D No because the sample size should be as small as possible for most applications

A data set includes 106 body temperatures of healthy adult humans having a mean of 98 7 F and a standard deviation of 0 66 F Construct a 99 confidence interval estimate of the mean body temperature of all healthy humans What does the sample suggest about the use of 98 6 F as the mean body temperature Click here to view a t distribution table Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table What is the confidence interval estimate of the population mean F H F Round to three decimal places as needed What does this suggest about the use of 98 6 F as the mean body temperature A This suggests that the mean body temperature is lower than 98 6 F OB This suggests that the mean body temperature is higher than 98 6 F C This suggests that the moon h

ten A group of data items and their mean are given Find a the deviation from the mean for each of the data items and b the sum of the deviations in part a 46 46 48 51 51 51 52 53 56 56 Mean 51 Oa 5 5 3 0 0 0 1 2 5 5 b 0 Oa 5 5 3 0 0 0 1 2 5 b 26 Oa 5 5 3 0 0 0 1 2 5 5 b 26 Oa 5 5 3 0 0 0 1 2 5 b 0

2 Cost B Et Cost 3 c Co 1 Total B C Total 2 Cost Er Cost Inver 3 Send a mes 10 Part 1 of 2 3 points Required 1 Required 2 Prepare journal entries dated June 30 to record a goods transferred from weaving to sewing b goods transferred from sewing to finished goods c sale of finished goods and d cost of goods sold A C Required information B D No Date June 30 June 30 June 30 June 30 of incorrect for the work you have completed so far It does not indicate completion General Journal Work in process inventory Sewing Work in process inventory Weaving Accounts receivable Sales Finished goods inventory Work in process inventory Sewing Cost of goods sold Finished goods inventory Required 1 33 Required 2 Debit 2 362 750 x 2 276 000 x 5 350 000 2 286 000 x Credit 2 362 750 x 2 276 000 5 350 000 2 286 000 x Return to question

Twelve different video games showing alcohol use were observed The duration times of alcohol use were recorded with the times seconds listed below What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 75 sec Are the requirements all satisfied 83 15 551 51 0 59 177 0 2 215 45 What requirements must be satisfied Select all that apply A At least one observation must be above or below 75 sec B The sample observations must be a simple random sample C The conditions for a binomial distribution must be satisfied D Either the population is normally distributed or n 30 or both Are the requirements all satisfied 60 Q O A No The sample size is not greater than 30 the sample does not appear to be from a normally distributed population and there is not enough information given to determine whether the sample is a simple random sample OB No The conditions for a binomial distribution are not satisfied and there is not enough information given to determine whether the sample is a simple random sample OC Yes A normal quantile plot suggests that the sample is from a normally distributed population and there is enough information to determine that the sample is a simple random sample OD No The sample size is not greater than 30 the sample does not appear to be from a normally distributed population and there are no observations above 75 sec OE Yes A normal quantile plot suggests that the sample is from a normally distributed population and there are observations above and below 75 sec OF Yes The conditions for a binomial distribution are satisfied and there is enough information to determine that the pom

Part 1 of 2 3 points Required information Required 1 Compute the a cost of products transferred from weaving to sewing b cost of products transferred from sewing to finished goods and c cost of goods sold Hint Compute the total production costs in each department and then subtract the ending inventory to get the amount transferred out of each department 2 Prepare journal entries dated June 30 to record a goods transferred from weaving to sewing b goods transferred from sewing to finished goods c sale of finished goods and d cost of goods sold Complete this question by entering your answers in the tabs below Required 1 Required 2 Answer is complete but not entirely correct Compute the a cost of products transferred from weaving to sewing b cost of products transferred from sewing to finished goods and c cost of goods sold a Transferred from Weaving to Sewing b Transferred from Sewing to Finished Goods do cold 440 000 X 84 000 X 3 296 000

Students estimated the length of one minute without reference to a watch or clock and the times seconds are listed below Assume that a simple random sample has been selected Use a 0 10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds Does it appear that students are reasonably good at estimating one minute 70 65 250 79 38 64 62 71 41 97 19 90 62 66 62 Perform the test assuming that the requirements are met Identify the null and alternative hypotheses Ho H Type integers or decimals Do not round

Which of the following is not a characteristic of the t test Choose the correct answer below OA The t test is robust against a departure from normality OB The Student t distribution is different for different sample sizes OC The Student t distribution has the same general bell shape as the standard normal distrib OD The Student t distribution has a mean of t 0 and a standard deviation of s 1