This chapter extends the hypothesis testing to analyze difference between population proportions based on 2 or more samples, and to test the hypothesis of independence in the joint responses to 2 categorical variables. Can we provide a real world example for using the Chi-square test along with expectation of the outcomes?

Please respond to the short answer items using the below dataset. For any values with long decimals, please round to two decimal places.

X Y

7    16

5 2

6 1

3 2

4    9

What is the value of SP, SS_X, SS_Y, and Pearson correlation r?

For the regression equation Y = bX + a, what is the value of b?

For the regression equation Y = bX + a, what is the value of a?

For the regression equation, using the b and a values you calculated above, what is the expected value of Y when X = 8?

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=58.2σ=58.2. You would like to be 95% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?

Use a z* value accurate to TWO places for this problem. (Not z = 2)

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.

Give all answers rounded to 3 places after the decimal point, if necessary.

(a) Enter the expected frequencies below:

(b) What is the chi-square test-statistic for this data?
      Test Statistic: χ2=χ2=

(c) What is the critical value for this test of independence when using a significance level of αα = 0.10?
      Critical Value: χ2=χ2=  

A magazine uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers. Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Retailer A and Retailer B customers are shown below.

(a)

Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let μ₁ = population mean satisfaction score for Retailer A customers and μ₂ = population mean satisfaction score for Retailer B customers.)

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

(b)

Assume that experience with the satisfaction rating scale of the magazine indicates that a population standard deviation of 13 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

At a 0.05 level of significance what is your conclusion?

Reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.    Do not Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Do not reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

(c)

Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Round your answers to two decimal places.)

to

Which retailer, if either, appears to have the greater customer satisfaction?

The 95% confidence interval  ---Select--- is completely below contains is completely above zero. This suggests that the Retailer A has a  ---Select--- higher lower population mean customer satisfaction score than Retailer B.

You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : μ 1 = μ 2 H a : μ 1 ≠ μ 2 You obtain the following two samples of data.

sample 2

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

A newspaper reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 30 female consumers was $61.64. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20.

(a)

What is the point estimate (in dollars) of the difference between the population mean expenditure for males and the population mean expenditure for females? (Use male − female.)

$

(b)

At 99% confidence, what is the margin of error (in dollars)? (Round your answer to the nearest cent.)

$

(c)

Develop a 99% confidence interval (in dollars) for the difference between the two population means. (Use male − female. Round your answer to the nearest cent.)

$  to $

Consider the following data for two independent random samples taken from two normal populations.

(a)

Compute the two sample means.

Sample 1Sample 2

(b)

Compute the two sample standard deviations. (Round your answers to two decimal places.)

Sample 1Sample 2

(c)

What is the point estimate of the difference between the two population means? (Use Sample 1 − Sample 2.)

(d)

What is the 90% confidence interval estimate of the difference between the two population means? (Use Sample 1 − Sample 2. Round your answers to two decimal places.)

to

A distributor of computer parts purchases a specific component from a supplier in lots of 1000 units. The cost of purchasing a lot is $30,000. The supplier is known to supply imperfect lots. In other words, a lot received by the distributor may contain defective units. Historical data suggest that the proportion of defective units in a lot supplied by this supplier follows the following probability distribution:

The distributor inspects the entire lot for defective units before selling the units to PC repair shops at a price of $45 per unit. The inspection process is error-proof so all defective units in a lot are detected and replaced by the distributor. It costs $20 for the distributor to replace a defective unit. The distributor has recently learned that the supplier offers a guarantee policy through which the supplier will assume the cost of replacing defective units in excess of the first 100 faulty units found in a given lot at no cost. [This means that the first 100 defective units found in a lot are replaced by the distributor for $20 per unit; however, all additional defective unit (if any) found in a lot are replaced by the supplier at no cost to the distributor.] This guarantee policy may be purchased by the distributor prior to the receipt of a given lot at a cost of $1000 per lot. The distributor wants to determine whether it is worthwhile to purchase the supplier’s guarantee policy.

QUESTION TO BE ANSWERED:

Perform sensitivity analysis: Perform a one-way sensitivity analysis using PrecisionTree ® on the optimal decision by letting the cost of replacing a defective unit vary from $10 to $30 in 11 steps and the cost of purchasing the supplier's guarantee policy vary from $400 to $1600 in 7 steps. Comment on your findings.

1-Television viewers often express doubts about the validity of certain commercials. In an attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the true population proportion?

2- An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of the nine accounts selected. The number of errors found in each of techniques A and B is listed in the table below:

Select a 90% confidence interval for the true mean difference in the two techniques.

a) [0.261, 8.627]

b) [-4.183, 4.183]

c) [2.195, 6.693]

d) [3.050, 5.838]

e) [2.584, 6.304]

f) None of the above

A group of psychiatrists want to investigate if there is any difference in depression levels (measured on a scale from [0=not at all depressed] to [100=severely depressed]) in patients who have been treated for depression by being told to regularly exercise versus those who were given an oral medication, Contentica, to treat depression.

The researchers selected a sample of 15 patients who were told to regularly exercise and found that their mean depression level was a score of 48 with a standard deviation of 9.

The researchers also selected a sample of 14 patients who were given the medication Contentica and found that their mean depression level was a score of 54 with a standard deviation of 10.

Conduct an appropriate two-tailed hypothesis test (two independent samples t-test) on whether or not patients who regularly exercise have a differentdepression level than those who are prescribed the medication Contentica using an alpha (α) level of 0.01.

You will use the information above to complete the question parts below for a two independent samples t-test.

Part A: Which of the following represents the appropriate null hypothesis (H₀), given this research question of interest?

PART A ANSWER: H₀:                     

       [ Select ]                       ["μ1 = 15", "μ1 - μ2 = 0", "μ1 - μ2 = 54", "μ1 - μ2 = 48", "μ1 - μ2 ≠ 48"]      

Part B: Which of the following represents the appropriate alternative hypothesis (H₁), given this research question of interest?

PART B ANSWER: H₁:                     

       [ Select ]                       ["μ1 - μ2 ≠ 48", "μ1 - μ2 ≠ 14", "μ1 - μ2 ≠ 54", "μ1 ≠ 15", "μ1 - μ2 ≠ 0"]      

Part C: What is the degrees of freedom (df)associated with your test?

PART C ANSWER:                  

      [ Select ]                       ["21", "45", "10", "27", "54"]      

Part D: Which of the following represents the appropriate critical value(s), testing at an alpha level (α) of 0.01?

PART D ANSWER:                        

    [ Select ]                       ["-2.892 and 2.892", "-2.771 and 2.771", "-2.312 and 2.312", "-1.251 and 1.251", "3.85"]      

Part E: What is the pooled variance(s²_p) associated with your test? (rounded to the nearest hundredth)

PART E ANSWER:                  

      [ Select ]                       ["45.12", "315.81", "90.15", "76.43", "12.86"]      

Part F: What is the estimated standard error of x̄₁ - x̄₂ associated with your test? (rounded to the nearest hundredth)

PART F ANSWER:                      

      [ Select ]                       ["3.53", "4.16", "7.89", "2.98", "1.05"]      

Part G: What is the t-statistic associated with your test? (rounded to the nearest hundredth)

PART G ANSWER:                        

[ Select ]                       ["1.21", "5.47", "3.96", "2.85", "-1.70"]      

Part H: Given your test results, what is your decision about the null hypothesis?

PART H ANSWER:                         

   [ Select ]                       ["Reject the null", "Fail to reject (i.e., retain) the null"]      

Part I: The best interpretation of the appropriate decision regarding the null hypothesis would be: "Based on our study, we                             [ Select ]                       ["have", "do NOT have"]         enough evidence to conclude that patients who regularly exercise do appear to have a different depression level than those who are prescribed the medication Contentica."

Part J: Which of the below represents a 99% confidence interval for the difference between the unknown population mean cholesterol levels of people on the new exercise regimen and people on the new medication?

PART J ANSWER:                      

       [ Select ]                       ["[-18.28 to -3.16]", "[-15.78 to 3.78]", "[-7.39 to 1.05]", "[-12.81 to 10.45]", "[3.45 to 9.82]"]      

You may need to use the appropriate appendix table or technology to answer this question.

The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.

(a)

Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.)

sample mean$  thousandsample standard deviation$  thousand

Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.)

sample mean$  thousandsample standard deviation$  thousand

(b)

What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private −Public.)

$  thousand

Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges.

We estimate that the mean annual cost to attend private colleges is $  more than the mean annual cost to attend public college

(c)

Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private − Public. Round your answers to one decimal place.)

$  thousand to $  thousand

http://lectures.mhhe.com/connect/0077837304/Excel/Ch15/Running.xlsx

Consider the following hypothesis test.

H₀: μ_d ≤ 0

H_a: μ_d > 0

(a)

The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.)

(b)

Compute

d.

(c)

Compute the standard deviation

s_d.

(d)

Conduct a hypothesis test using

α = 0.05.

Calculate the test statistic. (Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that

μ_d > 0.

Do not Reject H₀. There is sufficient evidence to conclude that

μ_d > 0.

     Do not reject H₀. There is insufficient evidence to conclude that

μ_d > 0.

Reject H₀. There is insufficient evidence to conclude that

μ_d > 0.

A global research study found that the majority of​ today's working women would prefer a better​ work-life balance to an increased salary. One of the most important contributors to​ work-life balance identified by the survey was​ "flexibility," with 42 42​% of women saying that having a flexible work schedule is either very important or extremely important to their career success. Suppose you select a sample of 100 100 working women. Answer parts​ (a) through​ (d). a. What is the probability that in the sample fewer than 50 50​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.) b. What is the probability that in the sample between 35 35​% and 50 50​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.) c. What is the probability that in the sample more than 43 43​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.) d. If a sample of 400 400 is​ taken, how does this change your answers to​ (a) through​ (c)? The probability that in the sample fewer than 50 50​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing . The probability that in the sample between 35 35​% and 50 50​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing . The probability that in the sample more than 43 43​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing .