Statistics Questions

The company would like your help in making a recommendation on the ideal mean setting that should be set for each vending machine so that the cups do not overflow or underfill Based on your findings from Part 1 decide a mean setting and a standard deviation you would recommend for the company Remember each cup holds 8 ounces The company would like to reduce the variability and keep the standard deviation low to ensure that most of the cups are not overflowing or underfilling Provide appropriate graphical and numerical evidence to support your recommendation Mean 8 23 Deviation 47 Part 3 Extra Practice stool The company wanted to compare two vending machine reports as part of a quality control check Use the data in Attachment B tab 2 to compare with the first vending machine in Attachment A Remember each cup holds 8 ounces Find the mean and standard deviation of the 2nd vending machine and compare it to the first machine How does 95 of the data for machine A compare with 95 of the data from machine B Which machine is more accurate in your opinion Why

Suppose lengths of text messages are normally distributed and have a known population standard deviation of 3 characters and an unknown population mean A random sample of 22 text messages is taken and gives a sample mean of 31 characters What is the correct interpretation of the 90 confidence interval Select the correct answer below We estimate that 90 of text messages have between 29 95 and 32 05 characters O We estimate with 90 confidence that the true population mean is between 29 95 and 32 05 characters We estimate with 90 confidence that the sample mean is between 29 95 and 32 05 characters

What is an explicit formula for the sequence a 1 5 a n 9 a n 1 7 a n 5 9 a n 5 9 1 a n 9 5 n 1 a n 9 5 B A

2 A sequence is defined recursively as j 1 2 178 j n 2 9j n 1 What is an explicit formula for the seq Ajn 2 178 2 9 Jn 2 178 2 9 in 2 178 2 9 n Din 2 178 2 9 1

What is 6 5 B 0 2 1 0 D 2 8 2 5 rounded to the nearest te

he following scenario to answer parts A C A theater has 19 rows of seats There are 22 seats in the first row 26 seats in the second row 30 seats in the third row an so on Part A Write an arithmetic or geometric sequence to model the situation Write both the explicit and recursive forms Explicit BUFE EXA ecursive

5 A geometric sequence has terms a 3 25 and a 5 1 What Is a 8

Given 20 26 32 38 44 What is the common difference for this Arithmetic Sequence d Write the equation formula for the given Arithmetic Sequence Do not use the space bar when typing your answer Find the 15th term of this Arithmetic Sequence 104 015

13 Use the sequence below to answer each question 8 25 10 4 Part A Create a geometric sequence function Make sure to use f n notation 5 Part B Find the 7th term in the sequence write as a FRACTION

A bicycle rental company charges a one time fee of 15 plus 4 for every hour of rental Part A Which recursive formula correctly models the cost in dollars of a rental for n hours a 1 4 a n a n 1 15 a 1 19 ain a n 1 15 a 1 19 a n a n 1 4 Part B How much will the bicycle rental cost in dollars for 7 hours Xa

What is the sum of the first 14 terms of the sequence an 11 n 1 327

B And the explicit formula for the given sequence 1 5 25 125 a 3 a 5 1 n a 3 5 1 9 2 5 1 1

Hind the sum of the first 3 terms in the geometric sequence with this first term and common rati a 12 r 0 2 Answer Note Round your answer to the nearest tenth a

The explicit formula shown is used to generate a sequence of numbers 15 5 n 1 Find the 21st term of the sequence 021

a The fifth term of an arithmetic sequence is 18 and the 11th term is 60 What is a rule for the sequence f n 10 7 n 1 f n 6 6 n 1 f n 7 10 n 1 f n 6 6 n 1 b Using the formula above find a G

Suppose lengths of text messages are normally distributie and have a known population standard deviation of 3 characters and an unknown population mean Arandon Sample of 20 text messays is taken and Sample mean of 31 characters gives a Identify the parameters needed to calculate a confidence interval at the 90 confidence level Then find the confidence interval 20 10 1 982 1 645 use the common z values given above Round the final answer to two decimal places if necessary IX 100 x 6 Z 0 05 Z 0 005 2 0 01 20 005 1 960 2 324 2 574 z g

The following are the annual incomes in thousands of dollars for 25 randomly chosen U S adults employed full time 30 32 33 34 34 36 37 38 38 39 39 41 42 42 43 44 47 48 49 52 52 60 84 100 118 Send data to calculator Frequency 20 15 10 5 0 16 Send data to Excel 6 Answer the questions below 1 45 65 85 105 Annual income in thousands of dollars 1 a Which measures of central tendency do not exist for this data set Choose all that Mean Median Mundo a Which measures of central tendency do not exist for this data set Choose all that apply 1 b Suppose that the measurement 118 the largest measurement in the data set were replaced by 156 Which measures of central tendency would be affected by the change Choose all that apply c Suppose that starting with the original data set the smallest measurement were removed Which measures of central tendency would be changed from those of the original data set Choose all that apply 125 Mean Median Mode All of these measures exist Mean Median Mode None of these measures Mean Median Mode None of these measures Sa 2023 McGraw Hill LLC All Rights Reserves

Use the given information about the geometric sequence to find the value of the specified term a 1 125 T 0 8 Find a 9 Enter the correct number in the box Round to the nearest thousandth if necessary Show Hints

minutes To test this claim a random sample of 70 completion times under new management was taken by the analyst The sample had a mean of 15 2 minutes Can we support at the 0 01 level of significance the claim that the population mean completion time under new management is less than 15 4 minutes Assume that the population standard deviation of completion times has not changed under new management Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your responses as specified below If necessary consult a list of formulas 1 91 F a State the null hypothesis Ho and the alternative hypothesis H H 0 b Determine the type of test statistic to use Choose one Y 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 P Search x 7 D X 0 0 OSO O d Find the critical value Round to three or more decimal places 0 e Can we support the claim that the population mean completion time under new management is less than 15 4 minutes S 2 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 5 P Q DO N 2023 McGraw Hilll LLC All Rights Reserved Terms of Use Privacy Center Save For Later X OSO 020 Submit Assi O O O

Translate the given recursive formula into an explicit formula a 1 18 a n a n 1 9 Enter the correct simplified expression in the box Show Hints a n E 7 8 9

ve formula for the geometric sequence with the two given terms a3 1296 as Enter the correct values in the boxes a1 M Show Hints an 7 8 9

What is the 14th term of the sequence Round your answer to six decimal places 120 90 Ta n 60 30 0 1 125 2 50 3 20 2 3 4 8 5 3 2 6 1 28 4 5 6 77 Enter the correct number in the box

Find the recursive formula for the arithmetic sequence with the two given terms f 7 33 f 20 112 3 Show Hints Of 1 3 6 f n f n 1 6 3 Of 1 3 5 f n f n 1 6 1 Of 1 3 6 f n f n 1 6 1 Of 1 3 5 f n f n 1 6 3

6 12 24 48 96 192 Show Hints O an 6n O an 6 2 1 Oa 25 9n of this sequence

A researcher collected sample data for 11 middle aged women The sample had a mean serum cholesterol level measured in milligrams per one hundred milliliters of 190 4 with a standard deviation of 8 1 Assuming that serum cholesterol levels for middle aged women are normally distributed find a 90 confidence interval for the mean serum cholesterol level of all women in this age group Give the lower limit and upper limit of the 90 confidence interval Carry your intermediate computations to at least three decimal places Round your answers to one decimal place If necessary consult a list of formulas Lower limit Upper limit S

Suppose weights in pounds of dogs in a city are normally distributed and have a known population standard deviation of pounds and an unknown population mean A random sample of 17 dogs is taken and gives a sample mean of 30 pounds Find the confidence interval for the population mean with a 80 confidence level Z0 10 1 282 OW Z0 05 1 645 Use the common z values given above Round the final answer to two decimal places Z0 025 1 960 Z0 01 2 326 Z0 005 2 576

mination periods indays forgrass Seed are normally distributed with a population standard deviation of 5days and an unknown population mean If a random Sample of 17 types of grass Seed is taken and results in a sample mean of 52 days find a 80 confidence interval for the population mean 20 10 1 282 Z 0 05 2 0 025 2 0 01 2 0005 1 645 2 326 2 574 Select the current answer below D 50 45 53 55 3 50 01 53 99 3 49 85 54 15 49 62 54 38 49 18 54 82 48 88 55 12

a Consider a t distribution with 11 degrees of freedom Compute P t 1 93 Round your answer to at least three decimal places P 1 1 93 b Consider a t distribution with 7 degrees of freedom Find the value of c such that P c t c 0 90 Round your answer to at least three decimal places c 0 X

Here are the numbers of calls received during 21 randomly chosen hours at a customer support service 1 3 6 7 8 9 11 11 11 12 13 13 14 14 14 17 17 18 19 22 23 Send data to calculator Frequency 10 8 6 4 2 0 0 2 5 Send data to Excel 4 Answer the questions below 10 15 Number of calls a For these data which measures of central tendency take more than one value Choose all that appl 4 20 2 Mean Median Mode 25

Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it If 5 Colonials games are chosen at random what is the probability that exactly 2 of those games are won by the Colonials Round your response to at least three decimal places If necessary consult a list of formulas

A movie studio wishes to determine the relationship between the revenue from rental of comedies on streaming services and the revenue generated from the theatrical release of such movies The studio has the following bivariate data from a sample of fifteen comedies released over the past five years These data give the revenue x from theatrical release in millions of dollars and the revenue y from streaming service rentals in millions of dollars for each of the fifteen movies Also shown are the scatter plot and the least squares regression line for the data The equation for this line is y 3 13 0 16x Theater revenue x in millions of dollars 25 6 48 8 43 8 62 1 27 7 31 2 12 9 7 7 25 9 66 1 1 1 25 9 66 1 15 0 20 8 29 0 59 9 36 5 Send data to calculator Rental revenue y in millions of dollars 7 4 16 1 7 5 10 3 11 9 5 6 10 1 2 2 9 2 10 5 Send data to Excel 9 2 10 5 1 8 4 8 3 6 16 6 12 3 Based on the studio s data and the regression line complete the following Rental revenue in millions of dollars 16 14 12 10 keni in mill X 26 X X xx Theater revenue in millions of dollars b According to the regression equation for an increase of one million dollars in theater revenue there is a corresponding increase of how many million dollars in rental revenue a For these data values for theater revenue that are less than the mean of the values for theater revenue tend to be paired with values for rental revenue that are Choose one the mean of the values for rental revenue X

Location Pet shelter Number of students 6 17 9 18 Work this semester Each student is volunteering at one of four locations Here is a summary Library Hospital Tutoring center Three students from the club are selected at random one at a time without replacement What is the probability that the first two students volunteer at the pet shelter and the third volunteers at the library Do not round your intermediate computations Round your final answer to three decimal places If necessary consult a list of formulas

The pages per book in a library are normally distributed with a population standard deviation of 33 pages and an unknown population mean A random sample of 16 books is taken and results in a sample mean of 334 pages What is the correct interpretation of the 99 confidence interval Select the correct answer below We estimate that 99 of the books in the library have between 312 75 and 355 25 pages O We estimate with 99 confidence that the sample mean is between 312 75 and 355 25 pages O O We estimate with 99 confidence that the true population mean is between 312 75 and 355 25 pages

An existing inventory for a test measuring self esteem indicates that the scores have a standard deviation of 10 A psychologist gave the self esteem test to a random sample of 150 individuals and their mean score was 60 Construct a 90 confidence interval for the true mean of all test scores Then give its lower limit and upper limit Carry your intermediate computations to at least three decimal places Round your answers to one decimal place If necessary consult a list of formulas Lower limit Upper limit X

cles The company that manufactures ballpoint pens sele samples of pens on each of 18 days The company recorded for each sample the number of defective pens in the sample Here are their data 2 2 2 2 3 3 3 3 5 6 6 6 7 10 11 14 15 17 Send data to calculator Frequency 8 6 4 2 0 0 8 Continue Answer the questions below Send data to Excel 5 a Which measures of central tendency do not exist for this data set Choose all that 2 8 12 16 Number of defective pens out of 1000 0 2 0 typic Question 5 of 19 1 point Question Attempt 1 of 1 2 2 Answer the questions below Mean Median 4 12 16 Number of defective pens out of 1000 a Which measures of central tendency do not exist for this data set Choose all that apply b Suppose that the measurement 17 the largest measurement in the data set were replaced by 40 Which measures of central tendency would be affected by the change Choose all that apply 20 2 c Suppose that starting with the original data set the largest measurement were removed Which measures of central tendency would be changed from those of 1 20 Mean Median Mode All of these measures exist Mean Median Mode None of these measures Mean Median Mode Save For Later 2023 McGraw Hill LLC All Rights Reserved Terms of Use Pr

A study of college football games shows that the number of holding penalties assessed has a mean of 2 3 penalties per game and a standard deviation of 0 8 penalties per game What is the probability that for a sample of 40 college games to be played next week the mean number of holding penalties will be 2 05 penalties per game or less Carry your intermediate computations to at least four decimal places Round your answer to at least three decimal places

normally distributed with a population ook in a library are Standard deviation of 33 pages and a unknown population mean Arandom sample of 16 books is taken and results in a sample mean of 334 pages Identify the parameters needed to calculate a confidence interval at the 99 confidence level Then find the confidence interval ZO 10 20 05 20 095 Z0 01 20 005 1 98 2 1 645 1 960 2 326 2 576 x 61 za

3 A restaurant sent out a survey to determine how long customers are willing to wait for a table on Friday night versus Saturday night Results are shown in the table below Table Wait Time Survey Results Number of Respondents 80 60 50 THE TIT 40 20 70 75 20 46 64 38 25 45 33 43 30 35 Number of Minutes 20 40 40 9 17 45 Friday Night Saturday Night A What does the chart indicate about how long people are willing to wait on either night B What does the chart indicate about how long people are willing to wait on Friday night versus Saturday night C How many responding people are willing to wait for 30 minutes on Friday night D How many responding people are willing to wait 40 minutes on a Saturday night E How many more people are willing to wait 25 minutes on Saturday versus Friday F How many fewer people are willing to wait 30 minutes versus 25 minutes on a Friday G CALCULATOR CHALLENGE On average how many minutes longer are customers willing to wait for a table on Saturday night than on a Friday night Round your answer to the nearest

The weights in pounds of dogs in a city are normally distributed with a population standard deviation of 2 pounds and an unknown population mean A random sample of 16 dogs is taken and results in a sample mean of 28 pounds What is the correct interpretation of the confidence interval Select the correct answer below O We can estimate that 90 of the dogs in the city have a weight that lies between 27 18 and 28 82 pounds We can estimate with 90 confidence that the sample mean weight of dogs in the city is between 27 18 and 28 82 pounds O We can estimate with 90 confidence that the true population mean weight of dogs in the city is between 27 18 and 28 82 pounds CV MORE INSTRUCTION SUBMIT

A psychologist is studying the self image of smokers as measured by the self image SI score from a personality inventory She would like to examine the mean SI score u for the population of all smokers Previously published studies have indicated that the mean SI score for the population of all smokers is 82 and that the standard deviation is 15 but the psychologist has good reason to believe that the value for the mean has decreased She plans to perform a statistical test She takes a random sample of SI scores for smokers and computes the sample mean to be 72 Based on this information complete the parts below a What are the null hypothesis Ho and the alternative hypothesis H that should be used for the test Ho H b Suppose that the psychologist decides not to reject the null hypothesis What sort of error might she be making Choose one c Suppose the true mean SI score for all smokers is 68 Fill in the blanks to describe a Type II error A Type II error would be Choose one the hypothesis that u is Choose one Choose one when in fact u is Choose one equal to 15 equal to 82 less than 15 less than 82 Check O N X XI OSO 0 0 Save For Later O Submit A

abgs are normally distributed with a standard deviation of a pounds and an unknown Population mean Arandom Sample of 16 dogs is taken and results in a sample mean of 28 pounds Identify the parameters needed to calculate a confidence interval at the 90 confidence level Then find the confidence interval COS Zoo Z 0 05 2 0 025 Zool 20 005 1 282 1 645 1 960 2 326 2 576 1237 use the common z values given above Round the final answer to two decimal place x n za 18

A financial analyst is examining the relationship between stock prices and earnings per share She chooses fifteen publicly traded companies at random and records for each the company s current stock price and the company s earnings per share reported for the past 12 months Her data are given below with x denoting the earnings per share from the previous year and y denoting the current stock price both in dollars Based on these data she computes the least squares regression line to be y 0 225 0 043x This line along with a scatter plot of her data is shown below Check Earnings per share x in dollars 15 23 27 19 17 38 22 17 39 39 43 38 59 64 40 79 57 54 37 77 33 93 41 22 Current stock price y in dollars 37 77 33 93 41 22 50 28 30 33 29 04 Question 5 of 9 1 point Question Attempt 2 of 3 43 38 59 64 40 79 57 54 0 40 0 99 0 58 0 74 1 04 1 56 2 12 1 13 2 89 1 55 1 70 1 73 Send data to calculator V 1 56 2 12 1 13 2 89 1 55 1 70 1 73 1 70 1 37 0 74 Send data to Excel Current stock price in dollars 0 5 Current stock in dollars Based on the analyst s data and regression line complete the following 10 20 16 x x X x Earnings per share in dollars x a For these data current stock prices that are greater than the mean of the current stock prices tend to be paired with values for earnings per share that are Choose one the mean of the values for earnings per share b According to the regression equation for an increase of one dollar in earnings per share there is a corresponding increase of how many dollars in current stock price Save For Later X Submit As Javi

ivariate data for the quantitative variables x and y are given in the table below These data are plotted in the scatter plot shown next to the table the scatter plot sketch an approximation of the least squares regression line for the data COLL X y 7 2 5 8 9 0 9 9 7 6 8 4 4 5 3 5 6 5 5 2 7 3 8 4 2 8 2 0 4 8 4 9 8 6 9 4 3 5 2 7 6 8 8 0 4 1 1 5 5 3 4 5 6 1 6 5 5 7 7 0 5 0 3 8 8 1 8 5 3 2 3 1 11 10 9 8 6 5 3 24 1 0 1 2 3 4 5 6 xxx 7 B x 9 10 X S

In examining per capita incomes for U S states over time one often finds that poor states tend to stay poor and wealthy states tend to stay wealthy So predictions about later years may sometimes be made from knowledge of previous years Consider the 1999 per capita income for a state denoted by y and its 1980 per capita income denoted by x The following bivariate data give the per capita income in thousands of dollars for a sample of fifteen states in the years 1980 and 1999 source U S Bureau of Economic Analysis Survey of Current Business May 2000 The data are plotted in the scatter plot in Figure 1 Colorado New Mexico Virginia New York Arizona Louisiana Hawail Michigan Arkansas Oregon Ohio Wisconsin Alabama Maine lowa Arkansas Oregon Ohio Wisconsin Alabama 1980 per capita 1999 per capita income x income y in 1000s in 1000s 10 8 8 4 10 2 11 1 9 6 8 8 11 5 10 4 7 6 10 2 10 1 10 2 7 9 8 4 9 7 Maine Lowa Send data to calculator 7 6 10 2 10 1 10 2 7 9 8 4 9 7 31 7 22 1 29 5 33 9 25 3 22 8 27 8 27 8 22 1 27 1 27 1 27 4 22 9 25 0 25 7 22 1 27 1 27 1 27 4 22 9 25 0 25 7 Send data to Excel woorde vad 6661 50001 Figure 1 34 32 1980 per capita income in 1000s Figure 1 20 1980 per capita income in 1000s a What is the value of the slope of the least squares regression line for these data Round your answer to at least two decimal places Expa ol b What is the value of the y intercept of the least squares regression line for these data Round your answer to at least two decimal places EB The value of the sample correlation coefficient r for these data is approximately 0 854 Answer the following Carry your intermediate computations to at least four decimal places and round your answers as specified below If necessa list of formulas 183

GAS The GAS which is a scale from 0 to 10 measures the general anxiety of an individual with higher GAS scores corresponding to more anxiety Dr Elbod s assessment of anxiety is based on a variety of measurements both physiological and psychological We re interested in making predictions about individuals sleep behavior based on their GAS scores The bivariate data below give the GAS score denoted by x and the number of hours of sleep last night denoted by y for each of the fifteen adults in a study The least squares regression line for these data has equation y 8 21 0 24x This line along with a scatter plot of the sample data is shown below GAS score x 3 0 3 8 3 4 4 9 6 0 7 9 6 9 9 0 0 8 1 6 0 8 1 6 8 0 9 1 6 4 2 0 4 0 Sleep time y in hours Question 6 of 9 1 point Question Attempt 1 of 3 Send data to calculator 6 8 8 4 7 5 6 4 7 7 5 7 6 4 5 7 7 0 9 0 7 0 9 0 7 4 6 2 6 0 8 0 6 8 Send data to Excel Sleep time In hours 10 x Based on the study s data and the regression line answer the following x b What was the observed sleep time in hours when the GAS score was 7 9 x GAS score X a From the regression equation what is the predicted sleep time in hours when the GAS score is 7 9 Round your answer to one or more decimal places X Espai 2 THE R G

The population standard deviation for the scores of a standardized test is 5 points If we want to be 95 confident that the sample mean is within 2 points of the true population mean what is the minimum sample size that should be taken Z0 05 Z0 025 Z0 01 Z0 005 1 645 1 960 2 326 2 576 Use the table above for the z score and be sure to round up to the nearest integer Provide your answer below test scores ZO 10 1 282

Suppose heights of dogs in inches in a city are normally distributed and have a known population standard deviation of 7 inches and an unknown population mean A random sample of 15 dogs is taken and gives a sample mean of 34 inches Find the confidence interval for the population mean with a 99 confidence level Provido Z0 10 1 282 Use the common z values given above Round the final answer to two decimal places holow Z0 05 1 645 Zo 025 1 960 Z0 01 2 326 Z0 005 2 576

Suppose the total snowfalls per year in a city are normally distributed If the population standard deviation is 13 inches what minimum sample size is needed to be 95 confident that the sample mean is within 4 inches of the true population mean ZO 10 Z0 05 Z0 025 Z0 01 Z0 005 1 282 1 645 1 960 2 326 2 576 Use the table above for the z score and be sure to round up to the nearest integer Provide your answer below

mally distributed such that 0 1 369 A sample of ds in football league 49 tight ends was randomly selected and the weights are given below Use excel to calculate the 95 confidence Interval for the mean Weight of all tight ends in this league Round your answers to two decimal places and Use ascending order Weight 300 294 155 270 218 240 150 364 298 167 297 299 221 266 261 301 269 267 219 165 198 359 240 263 171 169 259 196 197 268 271 200 295 199 260 363 264 241 220 265 262 343 321 302 364 296 170

give the revenue x from theatrical release in millions of dollars and the revenue y from streaming service rentals in millions of dollars for each of the fifteen movies Also shown are the scatter plot and the least squares regression line for the data The equation for this line is y 3 11 0 15x Theater revenue x in millions of dollars Question 5 of 9 1 point Question Attempt 1 of 3 7 0 43 9 66 4 13 5 20 8 49 9 28 1 60 5 Send data to calculator Rental revenue y in millions of dollars Send data to Excel Based on the studio s data and the regression line complete the following in millions of dollars 27 4 61 8 26 2 36 8 26 5 14 2 31 0 7 0 43 9 66 4 13 5 20 8 10 0 2 0 7 3 9 8 10 5 5 2 16 1 2 1 15 5 a For these data values for theater revenue that are less than the mean of the values for theater revenue tend to be paired with values for rental revenue that are Choose one the mean of the values for rental revenue rendct y in millions of dollars 11 2 9 9 7 1 12 6 8 0 2 1 5 9 2 0 7 3 9 8 10 5 5 2 Renta in millio b According to the regression equation for an increase of one million dollars in theater revenue there is a corresponding increase of how many million dollars in rental revenue Rental revenue in millions of dollars 18 164 14 xx 12 10 Theater revenue in millions of dollars x x x X X xx X 5 Javier V Espas C