Statistics Questions

Part 1 of 2 a Compute the expected frequencies under the null hypothesis Round your answers to two decimal places Siblings 0 1 2 3 4 More than 4 0 177 55 121 67 57 11 1 61 25 17 30 31 08 180 03 58 35 104 81 47 01 7 39 44 Number of Children 19 85 2 103 36 70 84 33 25 3 35 66 13 94 4 16 00 8 28 27 93 27 55 31 77 18 88 1 8 86 9 50 More than 4 5 00 16 87 16 64 11 40 5 35 5 74

A recent study examined the effects of carbon monoxide exposure on a group of construction workers The following table presents the numbers of workers who reported various symptoms along with the shift morning evening or night that they worked Morning Shift Night Shift Evening Shift 10 19 10 33 22 8 16 11 8 10 9 11 Influenza Headache Weakness Shortness of Breath Send data to Excel Test the hypothesis of independence Use the a 0 05 level of significance and the P value method with the TI 84 Plus calculator What do you conclude Part 0 4 Part 1 of 4 State the null and alternate hypotheses Ho The shift and reported symptoms Choose one independent H The shift and reported symptoms Choose one independent tort X E E dob

Do college students enjoy playing sports more than watching sports A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it The results of the study are shown below Playing Vs Watching Sports Play 3 1 2 1 8 29 2 29 Watch 1 2 1 1 9 1 10 1 2 7 Assume a Normal distribution What can be concluded at the the a 0 10 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 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 Select an answer the null hypothesis The results are statistically significant at a 0 10 so there is sufficient evidence to conclude that the ten students that were surveyed rated playing sports higher than watching sports on average The results are statistically significant at a 0 10 so there is sufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports The results are statistically insignificant at a 0 10 so there is insufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports The results are statistically insignificant at a 0 10 so there is statistically significant evidence to conclude that the population mean rating for playing sports is equal to the population mean rating for watching sports

The standard deviation for the resting heart rates of Rio Hondo Students was 12 beats per minute bpm The actual sample data is below 61 63 64 65 65 67 71 72 73 74 75 77 79 80 81 82 83 83 84 85 86 86 89 95 95 Based on this sample is there enough evidence to say that the standard deviation of the resting heart rate for students in this class is different from 12 bpm Use a 0 05 The null and alternative hypothesis would be 9 Ho 12 Ho 77 4 Hoo 12 Ho p 0 48 Ho H 77 4 H 0 12 H p0 48 H 9 H 12 O The test is two tailed right tailed left tailed Based on a sample of 25 games The test statistic is to 3 decimals The p value is to 3 decimals Based on both the p value method and the classical method we Reject the null hypothesis

Do shoppers at the mall spend more money on average the day after Thanksgiving compared to the day after Christmas The 58 randomly surveyed shoppers on the day after Thanksgiving spent an average of 127 Their standard deviation was 43 The 52 randomly surveyed shoppers on the day after Christmas spent an average of 112 Their standard deviation was 32 What can be concluded at the a 0 05 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 a e Based on this we should f Thus the final conclusion is that Select an answer Select an answer please show your answer to 3 decimal places Please show your answer to 4 decimal places Select an answer the null hypothesis The results are statistically insignificant at a 0 05 so there is insufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is more than the population mean amount of money that day after Christmas shoppers spend The results are statistically insignificant at a 0 05 so there is statistically significant evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is equal to the population mean amount of money that day after Christmas shoppers spend The results are statistically significant at a 0 05 so there is sufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is more than the population mean amount of money that day after Christmas shoppers spend The results are statistically significant at a 0 05 so there is sufficient evidence to conclude that the mean expenditure for the 58 day after Thanksgiving shoppers that were observed is more than the mean expenditure for the 52 day after Christmas shoppers that were observed

You work for a soft drink company in the quality control division You are interested in the standard deviation of one of your production lines as a measure of consistency The product is intended to have a mean of 12 ounces and your team would like the standard deviation to be as low as possible You gather a random sample of 15 containers Estimate the population standard deviation at a 98 level of confidence Use 3 decimal places for all answers 12 02 11 99 12 15 11 79 11 88 11 98 12 02 11 99 11 96 12 03 11 74 11 93 11 95 12 1 12 1 Data checksum 179 63 a Find the sample standard deviation b Find the lower and upper x critical values at 98 confidence Lower Upper c Report your confidence interval for

The commercial for the new Meat Man Barbecue claims that it takes 9 minutes for assembly A consumer advocate thinks that the assembly time is higher than 9 minutes The advocate surveyed 11 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 10 1 minutes The standard deviation for this survey group was 3 9 minutes What can be concluded at the the a 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 g Thus the final conclusion is that please show your answe Please show your answer to 4 decimal places swer to 3 decimal places Select an answer the null hypothesis The data suggest that the population mean amount of time to assemble the Meat Man barbecue is not significantly higher than 9 at a 0 05 so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is higher than 9 The data suggest the population mean is not significantly higher than 9 at a 0 05 so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is equal to 9 O The data suggest the populaton mean is significantly higher than 9 at a 0 05 so there is statistically significant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is higher than 9

For each scenario listed below determine whether the scenario represents an Independent Samples or Dependent Samples Matched Pairs situation by placing the appropriate letter in the box provided a Comparing the incomes of 40 Democrats and 70 Republicans O Independent Samples O Matched Pairs b Comparing the LDL cholesterol for 50 soccer players and 50 basketball players O Matched Pairs Independent Samples c Comparing how many hours 70 students spend studying per week to how many hours they spend on their smartphone per week O Matched Pairs O Independent Samples d Comparing the days hibernated by 45 black bears in California and 45 polar bears in Alaska O Independent Samples O Matched Pairs

Suppose the 95 confidence interval 198 212 represents the mean number of eggs Henrietta the Hen lays per year The 95 confidence interval 220 246 represents the mean number of eggs Hannah the Hen lays per year a Based on the confidence intervals is it likely that Henrietta lays an average of 225 eggs in a year Yes all the interval values are greater than 225 O No 225 is not contained in the interval Yes 225 is not contained in the interval b Based on the confidence intervals can we conclude which hen likely lays more eggs in one year on average Yes Henrietta is more likely to lay more eggs on average Yes Hannah is more likely to lay more eggs on average No we are only 95 confident and the values are close

a Compute the expected frequencies Category Observed Part 1 3 Expected 63 Part 2 of 3 1 67 The P value is 2 45 36 3 13 9 4 55 72 b Find the P value Use Excel round to four decimal places

April May June July August September October November December Send data to Excel Part 0 2 28 33 34 43 Can you conclude that false alarms are not equally likely to occur in any month Use the a 0 01 level of significanc Part 1 of 2 38 29 44 34 45 a Find the P value Use Excel round to four decimal places

a 0 10 level of significance Part 1 of 2 a Find the P value Use Excel round to four decimal places The P value is 0 7727 Part 1 2 of observed frequencies differs from that given by the expected frequencies Use Excel and the P value method use the Part 2 of 2 b Write a conclusion We Choose one Ho There Choose one enough evidence at the a 0 10 level of significance to say that the distribution of observed frequencies differs from that given by the expected frequencies Ella V Espar a G E 5 CL

Part 1 of 3 a How many students got a B How many got an A There were 8 B grades and 8 A grades Part 1 3 Part 2 of 3 b Which grades were given more often and less often than expected Grade A B More O Less X 3

Following are observed frequencies The null hypothesis is Ho P 0 35 P 0 20 P3 0 05 P4 0 4 Category 1 Observed 67 Part 0 3 Part 1 of 3 Can you conclude that the distribution of observed frequencies differs from that given by the null hypothesis Use the a 0 025 level of significance Category 2 45 a Compute the expected frequencies 1 3 13 Observed 67 2 4 55 45 3 13 4 55 X

For the following observed and expected frequencies Observed 41 Expected 45 Part 0 2 Part 1 of 2 22 26 Can you conclude that the distribution of observed frequencies differs from that given by the expected frequencies Use Excel and the P value method use the a 0 10 level of significance The P value is 40 44 26 28 X a Find the P value Use Excel round to four decimal places 31 28 3 E OL E

Grade distribution A statistics teacher claims that on the average 10 00 of her students get a grade of A 20 00 get a B 10 00 get a C 35 00 get a D and 25 00 get an F The grades of a random sample of 100 students were recorded The following table presents the results Category A B C D F Observed 8 8 15 46 23 Can you conclude that the distribution of the grades differs from the teacher s claim Use the a 0 05 level of significance Part 0 3 Part 1 of 3 a How many students got a B How many got an A There were B grades and A grades Espa ol 8E0 2

The probability distribution of X the number of males with tinnitus ringing ears among 6 randomly selected males is as follows 0 aN P X a 0 57 1 exactly 4 0 25 2 0 1 3 0 03 b P X 2 or X 3 c P X 0 4 0 03 5 1 Use the random variable notation to express symbolically each of the following An event in which the number of males with tinnitus is exactly 4 The probability of an event in which the number of males with tinnitus is 2 Use the above probability distribution table to find the following a P X 5 0 01 0 01 The probability of an event in which the number of males with tinnitus is exactly 4 is equal to 0 03 Round the answer to 2 decimals Total Round the answer to 2 decimals 1 Round the answer to 2 decimals

The following refer to the following data set 91 5 91 5 77 8 65 1 91 5 63 6 79 8 70 8 55 8 83 8 What is the arithmetic mean of this data set mean What is the median of this data set median What is the mode of this data set mode

a Find the following values Round to two decimal places as needed Q b Identify the box and whiskers pilot for this data modified as necessary 01 Median 3 0123 3 0 0 12 1 4 0 567 9 10 11 12 5 6 7 8 9 10 11 12 Q 6 7 8 9 10 11 12 IQR

A randomly selected card from a standard 52 card deck is noted The card is then replaced the deck is shuffled and a second card is selected and noted What is the probability that both cards are Aces chance that two Aces are randomly selected with replacement There is a

A boy owns 1 pairs of pants 5 shirts 8 ties and 6 jackets How many different outfits can he wear to school if he must wear one of each item He can wear different outfits

X 0 1 2 3 P x 0 1 0 25 0 05 0 6 Find the mean of this probability distribution Round your answer to one decimal

The table contains the number of M M s of each color that were found in a case M M Distribution Blue 467 P blue P brown P green P orange P red Brown 390 Find the probability of choosing each color based on this experiment Round to four decimal places if necessary P yellow Green 387 Orange 409 Red 435 Yellow 494 Total 2582

The class ranks of 20 students selected for a survey about cafeteria food at a high school are shown in the table below Freshman Use these data to complete each of these questions a Complete the frequency relative frequency table Class Rank Sophomore Junior Freshman Freshman Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Junior Freshman Senior Senior Sophomore Sophomore Freshman Freshman Sophomore Freshman Frequency Senior Junior Senior Relative Frequency in percent 1 1

date int 20210113 20210113 20210113 20210113 20210113 20210114 season startTime int chr 20202021 2021 01 13T22 30 00Z 20202021 2021 01 14T01 00 00Z 20202021 2021 01 14T00 00 00Z 20202021 2021 01 14T03 00 00Z 20202021 2021 01 14T03 30 0OZ 20202021 2021 01 15T00 00 00Z endTime chr 2021 01 14T00 53 50Z 2021 01 14T03 53 11Z 2021 01 14T02 50 09Z 2021 01 14T05 39 01Z 2021 01 14T06 10 19Z 2021 01 15T02 38 38Z status chr Final Final Final Final Final Final VTabbr HTabbr chr chr PIT CHI MTL VAN STL WSH PHI TBL TOR EDM COL BUF VT chr Pittsburgh Penguins Chicago Blackhawks Montr al Canadiens Vancouver Canucks St Louis Blues Washington Capitals

CQ1 Recall from lecture that a z score can be used to describe how many standard deviations an observed value is from the mean this sort of description is usually reserved for cases when the distribution of our attribute is fairly symmetrical We also mentioned that z scores are often used in calculations Type the equation in terms of z scores we can use to calculate the correlation coefficient r

The ages of the first 16 U S presidents at the time of their first inauguration are displayed below president Washington John Adams Jefferson Madison Monroe J Q Adams Jackson Van Buren W H Harrison Tyler Polk Taylor Fillmore Pierce Buchanan Lincoln a Make and label a histogram and boxplot for this data using GeoGebra Insert your histogram and boxplot in the add work box and type your titles and labels above and below the graphs Use the Export button in GeoGebra and the Insert Image button in the Add work box Use GeoGebra to compute each of the following summary statistics rounding to one decimal place if needed b median age 57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 100 years

B SECTION 4 1 4 1 Predicting Land Value Both scatterplots concern the assessed value of land with homes on the land and both depict the same observations A b If you were trying to predict the value of a parcel of land on which there is a home in this area would you be able to make a better pre diction by knowing the acreage or the number of rooms in the house Explain Source Minitab File Student 12 Assess a Which do you think has a stronger relationship with value of the land the number of acres of land or the number of rooms in the homes Why Value of Land thousands of dollars Value of Land thousands of dollars 140 100 80 60 120 100 80 120 40 140 60 40 1 0 5 0 7 5 2 3 Acreage 4 5 10 0 12 5 15 0 17 5 Rooms 6 4 2 Predicting Total Value of Property Both scatterplots con cern the total assessed value of properties that include homes and both depict the same observations a Which do you think has a stronger relationship with value of the prop erty the number of square feet in the home shown in part B of the figure or the number of fireplaces in the home shown in part A of the figure Why b If you were trying to predict the value of a property where there is a home in this area would you be able to make a better prediction by knowing the number of square feet or the number of fireplaces Explain A B Value of Car dollars Total Value thousands of dollars Total Value thousands of dollars 4 0 500 3 5 400 3 0 300 2 5 200 100 500 400 300 16000 14000 12000 10000 8000 6000 4000 2000 0 200 100 0 4 3 Car Value and Age of Student The scatterplot shows the age of students and the value of their cars according to the Kelley Blue Book Does it show an increasing trend a decreasing trend or very little trend Explain 500 1 2 3 4 5 Number of Fireplaces 6 1000 1500 2000 2500 3000 3500 Number of Square Feet 20 25 4 4 Shoe Size and GPA The figure shows a scatterplot of shoe size and GPA for some college students Does it show an increasing trend a decreasing trend or no trend Is there a strong relationship 30 35 40 45 50 Age of Student

Question 7 You work for a large farm with many fields of corn You are investigating the mass of a sample of ears of corn You gather the following data 8 pts 1 Details Mass g of ears of corn 12 9 13 2 13 8 13 9 14 0 14 1 14 9 15 1 15 2 15 4 15 4 16 3 17 7 19 4 19 5 20 0 20 1 20 6 21 9 22 2 22 4 26 7 28 2 31 2 Some of the masses in the sample seem much larger than the rest so you want to test for outliers Here are your summary Statistics Mean St Dev 18 5 5 01 Min Q1 Med Q3 Max 12 9 14 5 17 21 25 31 2 Apply the 1 5 IQR rule to search for outliers Calculate the lower and upper fences to 3 decimal places a IQR b Lower Fence c Upper Fence d Are there any outliers by the 1 5 IQR rule Enter yes or no Question Help Message instructor Add Work

4 28 See Saw The table gives data on the heights above ground of the left and right seats of a see saw in feet Assume the trend is linear calculate the correlation and explain what it shows Left 4 3 C Right 0 1

TRY 4 5 Weight Loss Example 1 The scatterplot shows the actual weight and desired weight change of some students Thus if a student weighed 220 and wanted to weigh 190 the desired weight change would be negative 30 Explain what you see In particular what does it mean that the trend is negative Desired Change in Weight pounds 20 10 0 10 20 30 40 50 60 70 100 120 140 160 180 200 220 240 260 Weight pounds

4 3 Car Value and Age of Student The scatterplot shows the age of students and the value of their cars according to the Kelley Blue Book Does it show an increasing trend a decreasing trend or very little trend Explain Value of Car dollars 16000 14000 12000 10000 8000 6000 4000 2000 0 a 20 25 30 35 40 45 T 50

Find the producers surplus at a price level of p 67 for the price supply equation below p S x 10 0 1x 0 0003x The producers surplus is Round to the nearest integer as needed

A manufacturer guarantees a product for 1 year The lifespan of the product after it is sold is given by the probability density function below where t is time in months 0 012e 0 012 ift20 f t 0 otherwise What is the probability that a buyer chosen at random will have a product failure A During the warranty B During the second year after purchase A What is the probability that the product will fail within one year Round to three decimal places as needed

Use a graphing calculator to graph the normal probability density function f x 1 o 2 H 400 and the standard deviation 200 Choose the correct graph below O A 0 800 100 by 0 0 03 0 002 5 OB 600 1000 100 by 0 0 03 0 002 Q S O C 0 800 100 by 0 0 004 0 0002 Q Q e x 20 O D that has the mean Q Q n 600 1000 100 by 0 0 001 0 0001 5

a 0 7 3 1 0 a 1 2 a 2 0 03 1 1 a 0 9 Suppose that the system shown in the above figure consists of parts whose time to failure has a pdf given by 9 3 1 20 20 with a given Calculate the probability that the system is functioning at time t 3

Clearly and neatly show all work for each problem Round all final answers to the nearest dollar Do not round intermediate work 1 Velma currently has a job that pays her 48 000 a year She is paid twice a month on the 5th and the 20th and wants to start saving for retirement and pay off her credit card Velma plans to contribute 7 5 of her pre tax income to her company s 401k Find how much of each paycheck Velma will be putting into the 401k If the 401k is compounded semi monthly at a rate of 3 2 find the balance in 30 years when Velma hopes to retire

2 Velma plans to put the unused portion of her paycheck towards paying off her credit card As of September 1st the beginning of her credit card payment cycle Velma s credit card balance was 3 200 During the course of the month Velma only uses her credit card once buying 40 worth of gas on September 8th The only other transactions on her credit card are her payments of 1 100 towards her credit card balance on the 5th and 20th Velma s card has a monthly interest rate of 2 Using the average daily balance method find her finance charge for the month of September Find Velma s balance as of October 1st

traditionally been 60 A policy maker claims that the proportion is less than 60 now that one of the recycling centers has been relocated If 125 out of a random sample of 245 residents in the community said they recycle is there enough evidence to support the policy maker s claim at the 0 05 level of significance 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 d Find the p value Round to three or more decimal places 0 e Is there enough evidence to support the policy maker s claim that the proportion of residents who recycle is less than 60 OYes No XI O X S 2 OSO 0 0 0 0 P Q G olo L 020 0 0

State the type of sample 1 A radio station asks to listeners to call in and give their opinion on the song just played 2 A Student selected books from each of the categories of Science fiction and history The number of pages in each book was identified 3 During the last presidential election CNN Conducted an exit poll at randomly Selected Polling station and all voters Were Surveyed as they left the premises when collecting data in a lake a researcher Stretches a rope across the lake and Collects Samples atevery interal of 5 meters To Testa New drug Subects were Trondmly selected to take part in

D list are pulse rate of 20 females Selected for a test 80 94 58 66 56 82 78 86 88 56 36 66 84 76 78 64 66 78 64 60 Construct a stem and leaf plot 700 344

list are pulse rate of 20 females Selected for a test 80 94 58 66 56 82 78 86 88 76 78 64 66 78 64 56 36 66 84 60 Construct a stem and leaf plot

econds of eruption of the old Faith ful exertion of the patioral gey parn 125 240 248 203 240 248 205 241 249 221 241 249 225 2242 250 229 242 251 233 242 252 233 243 253 235 243 253 236 244 255 236 244 255 287 245 256 238 245 257 238 245 258 239 246 262 240 246 264 240 248 A B create a histogram Class being agu Create a frequently table with the frist frequency polgon The

A New muscle relaxantin foil is available The lapse between administration of the drug beginning effects Of the druy is normally distributed with a mean of 38 minutes and a standard deviation of S minutes S PAX030 If the druge is administered to one person what is the per cent that the time it take f atet to go into effect is 25 minutes or less

Find the linear quadratic and logarithmic functions that best fit the data points 1 4 6 2 5 0 3 6 0 4 6 2 and 5 6 5 Which of the three functions best fits the data The linear function that best fits the data points is y 0 5x 4 16 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 quadratic 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

You have a friend that is taking statistics at another college They are struggling with confidence intervals and hypothesis testing What advice would you give your friend about how to know how to calculate the different types of intervals and hypothesis tests

You read an article which states that 80 of adults in your city have a high school diploma You do not believe this statement and decide to test it a Write the null and alternative hypotheses Ho p 0 8 Ha P Select 0 8 b Suppose that after you finished your study you committed a type I error Explain what that means in this context This means you Select the null hypothesis but the null hypothesis is Select context this means that you concluded that Select when in fact it is Select V In that

A marketing survey involves product recognition in New York and California Of 458 New Yorkers surveyed 183 knew the product white 176 out of 514 Californians knew the product At the 0 05 significance level test the claim that the recognition rates are the same in both states Ho PNew York PCalifornia Ha PNew York Select Test statistic Select p Value Select decision Select Conclusion There Select PCalifornia V evidence to make the conclusion that recognition rates are the same in both states

A survey was conducted to determine the average loss in home value in a certain community A random sample of 23 homes found a mean of 12130 with a standard deviation of 1400 Assume the necessary assumptions are met a Calculate a 98 confidence interval for the population mean loss in home value Select Type of interval We are 98 confident that the average loss in home value is between Select dollars b What is the margin of error Select Select and

A manufacturer makes steel rods that are supposed to have a mean length of 50 centimeters A retailer suspects that the rods are running short The mean length for a random sample of 34 rods was 48 4 centimeters with a standard deviation of 3 6 centimeters Test the claim that the mean length is less than 50 centimeters at a 0 05 Can the retailer conclude that the rods are running short Explain how you made your decision including any calculations you made