A survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. Using data from a sample of 42 credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). Using the difference data, with population 1 population 2, the sample mean difference was

d = $840,

and the sample standard deviation was

s_d = $1,122.

(a)

Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

H₀: _d < 0

H_a: _d = 0

H₀: _d 0

H_a: _d = 0

H₀: _d 0

H_a: _d > 0

H₀: _d 0

H_a: _d < 0

H₀: _d = 0

H_a: _d 0

(b)

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

What is the p-value? (Round your answer to four decimal places.)

Can you conclude that the population means differ? Use a 0.05 level of significance.

The p 0.05, therefore we cannot conclude that there is a difference between the annual population mean expenditures for groceries and for dining out.

The p 0.05, therefore we can conclude that there is a difference between the annual population mean expenditures for groceries and for dining out.

The p > 0.05, therefore we cannot conclude that there is a difference between the annual population mean expenditures for groceries and for dining out.

The p > 0.05, therefore we can conclude that there is a difference between the annual population mean expenditures for groceries and for dining out.

(c)

What is the point estimate (in dollars) of the difference between the population means?

$

What is the 95% confidence interval estimate (in dollars) of the difference between the population means? (Round your answers to the nearest dollar.)

$ to $

Which category, groceries or dining out, has a higher population mean annual credit card charge?

The 95% confidence interval ---Select--- is completely above contains is completely below zero. This suggests that the category with higher mean annual expenditure is ---Select--- groceries dining out .

3.

DETAILSASWSBE14 18.E.019.

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

Samples of starting annual salaries for individuals entering the public accounting and financial planning professions follow. Annual salaries are shown in thousands of dollars.

Public Accountant	Financial Planner
49.2	49.0
59.8	49.2
55.3	52.1
57.2	55.9
54.2	52.9
54.0	52.6
51.9	48.7
60.5	53.9
56.0	52.8
51.9	47.9

(a)

Use a 0.05 level of significance and test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planners.

State the null and alternative hypotheses.

H₀: The two populations of salaries are identical. H_a: The two populations of salaries are not identical.H₀: Median salary for public accountants Median salary for financial planners 0 H_a: Median salary for public accountants Median salary for financial planners < 0 H₀: Median salary for public accountants Median salary for financial planners > 0 H_a: Median salary for public accountants Median salary for financial planners = 0H₀: Median salary for public accountants Median salary for financial planners 0 H_a: Median salary for public accountants Median salary for financial planners > 0H₀: The two populations of salaries are not identical. H_a: The two populations of salaries are identical.

Find the value of the test statistic.

W =

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

p-value =

What is your conclusion?

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners. Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.

(b)

What are the sample median annual salaries (in $) for the two professions?

Public Accountants sample median=$

Financial Planners sample median=$

4.

DETAILSASWSBE14 18.E.023

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

Police records show the following numbers of daily crime reports for a sample of days during the winter months and a sample of days during the summer months.

Winter	Summer
17	27
20	17
15	24
19	31
22	17
20	26
11	23
19	37
16	27
20	17

Use a 0.05 level of significance to determine whether there is a significant difference between the winter and summer months in terms of the number of crime reports.

State the null and alternative hypotheses.

H₀: The two populations of daily crime reports are identical. H_a: The two populations of daily crime reports are not identical.

H₀: Median number of daily crime reports for winter Median number of daily crime reports for summer < 0

H_a: Median number of daily crime reports for winter Median number of daily crime reports for summer = 0

H₀: The two populations of daily crime reports are not identical. H_a: The two populations of daily crime reports are identical.

H₀: Median number of daily crime reports for winter Median number of daily crime reports for summer 0 H_a: Median number of daily crime reports for winter Median number of daily crime reports for summer < 0.

H₀: Median number of daily crime reports for winter Median number of daily crime reports for summer 0

H_a: Median number of daily crime reports for winter Median number of daily crime reports for summer > 0

Find the value of the test statistic.

W =

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

p-value =

What is your conclusion?

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.

Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.