11. Consider the following contingency table of observed frequencies. Complete parts a. through d. below.

a. Identify the null and alternative hypotheses for a chi-square test of independence with based on the information in the table. This test will have a significance level of

=0.025.

Choose the correct answer below.

A.

H0:

The variables R1, R2, C1, C2, and C3 are independent.

H1:

None of the variables are independent.

B.

H0:

The row and column variables are independent of one another.

H1:

The row and column variables are not independent of one another.

C.

H0:

The row and column variables are not independent of one another.

H1:

The row and column variables are independent of one another.

D.

H0:

The variables R1, R2, C1, C2, and C3 are independent.

H1:

At least one of the variables is not independent.

b, Calculate the expected frequencies for each cell in the contingency table.

		Column Variable
Row Variable	C1	C2	C3
R1	enter your response here	enter your response here	enter your response here
R2	enter your response here	enter your response here	enter your response here

(Round to two decimal places as needed.)

c. Calculate the chi-square test statistic.

2=enter your response here

(Round to two decimal places as needed.)

d. Determine the p-value. Using =0.025, state your conclusions.

p-value=enter your response here

(Round to three decimal places as needed.)

State your conclusions.

The p-value is (greater than, less than) =0.025, so(reject, do not reject) H0. There is (sufficient, insufficient) evidence to indicate that

(at least one of the variables is not independent

the row and column variables are independent of one another.

thevariablesR1,R1,C1,C2,andC3areindependent.

the row and column variables are not independent of one another.

none of the variables are independent.)

12.Suppose a credit card company would like to determine if the type of credit card influences the payment status of a customer's account. The following table indicates the card type for 200 randomly selected customers, along with the number of days their payments were overdue. Complete parts a. through c. below.

Card Type
Days Overdue	Standard	Gold	Platinum
30 days or less	75	36	31
31-60 days	14	9	8
61 days or more	12	9	6

a. Using =0.10, perform a chi-square test to determine if the credit card type and payment status are independent of one another. Identify the null and alternative hypotheses for a chi-square test of independence based on the information in the table. Choose the correct answer below.

A.

H0:

Credit card type and payment status are independent of one another.

H1:

Credit card type and payment status are not independent of one another.

B.

H0:

The variables Standard, Gold, Platinum, 30 days or less, 31-60 days, and 61 days or more are independent.

H1:

None of the variables are independent.

C.

H0:

The variables Standard, Gold, Platinum, 30 days or less, 31-60 days, and 61 days or more are independent.

H1:

At least one of the variables is not independent.

D.

H0:

Credit card type and payment status are not independent of one another.

H1:

Credit card type and payment status are independent of one another.

Find the chi-square test statistic.

2=enter your response here

(Round to two decimal places as needed.)

Using =0.10, find the chi-square critical value, 2.

2=enter your response here

(Round to two decimal places as needed.)

Determine the result of the test.

The test statistic 2 is

(greater than, less than) the critical value 2, so (reject, do not reject)

the ( null, alternative)

b. What conclusions can be made based on these results?

There is(sufficient, insufficient) evidence to indicate that

(At least one of the independent variables is not independent,

credit card type and payment status are not independent of each other,

credit card payment and status are independent of each other,

none of the variables were independent).

c. Determine the p-value using technology and interpret its meaning.

p-value=enter your response here

(Round to three decimal places as needed.)

Interpret the meaning of the p-value.

The p-value is the probability of observing a(test statistic, critical value) as extreme or more extreme than the one observed under the assumption that the (null hypothesis, alternative hypothesis) is true. A p-value less than the significance level means that the (critical value, test statistic) is (likely, unlikely) enough that the (null hypothesis, alternative hypothesis) should be rejected. For this test, the p-value is(greater than, less than) =0.10, so (reject, do not reject) the (null hypothesis, alternative hypothesis.) There is (insufficient, sufficient) evidence to indicate that

at least one of the variables is not independent.

none of the variables are independent

credit card type and payment status are independent of one another.

credit card type and payment status are not independent of one another.

13.

The table to the right shows the medal count for three countries following an international athletic event. Complete parts a. through c. below.	Medal
Country	Gold	Silver	Bronze
A	9	14	14
B	9	13	7
C	15	7	6

a. Using =0.025, perform a chi-square test to determine if the type of medal and the country that earned it are independent of one another. Identify the null and alternative hypotheses for a chi-square test of independence based on the information in the table. Choose the correct answer below.

A.

H0:

Type of medal and country that earned it are independent of one another.

H1:

The type of medal affects the country that earned it.

B.

H0:

Type of medal and country that earned it are not independent of one another.

H1:

Type of medal and country that earned it are independent of one another.

C.

H0:

Type of medal and country that earned it are independent of one another.

H1:

The country that earns the medal affects the type of medal.

D.

H0:

Type of medal and country that earned it are independent of one another.

H1:

Type of medal and country that earned it are not independent of one another.

Find the chi-square test statistic.

2=enter your response here

(Round to two decimal places as needed.)Using =0.025, find the chi-square critical value, 2.

2=enter your response here

(Round to two decimal places as needed.)

Determine the result of the test. Choose the correct answer below.

A.

Fail to reject

H0. The test statistic falls into the rejection region.

B.

Reject

H0. The test statistic does not fall into the rejection region.

C.

Reject

H0. The test statistic falls into the rejection region.

D.

Fail to reject

H0. The test statistic does not fall into the rejection region.

b. What conclusions can be made based on these results?

There is(sufficient, insufficient) evidence to indicate that

(type of medal and the country who earned it are not independent of each other,

the country who earns the medal affects the type of medal,

the type of medal affects the country who earned it,

type of medal and the country who earned it are independent of each other)

c. Determine the p-value using technology and interpret its meaning.

p-value=enter your response here

(Round to three decimal places as needed.)

Interpret the meaning of the p-value.

The p-value is the probability of observing a(test statistic, critical value) as extreme or more extreme than the one observed under the assumption that the (null hypothesis, alternative hypothesis) is true. A p-value less than the significance level means that the (critical value, test statistic) is (likely, unlikely) enough that the (null hypothesis, alternative hypothesis) should be rejected. For this test, the p-value is(greater than, less than) =0.025, so (reject, do not reject) the (null hypothesis, alternative hypothesis.) There is (insufficient, sufficient) evidence to indicate that

(type of medal and the country who earned it are not independent of each other,

the country who earns the medal affects the type of medal,

the type of medal affects the country who earned it,

type of medal and the country who earned it are independent of each other)

14. Suppose a marketing research firm would like to examine if the social networking site that a person primarily uses is influenced by his or her age. In a randomly drawn sample, 339 social network users were asked which site they primarily visited. These data are presented in the following table along with each person's age group. Complete parts a. through c. below.

Social networking site
Age group	Site a	Site b	Site c
2-17	25	13	2
18-34	100	20	14
35-54	91	17	17
55+	28	3	9

a. Using =0.025, perform a chi-square test to determine if age group and social networking site used are independent of one another. Identify the null and alternative hypotheses for a chi-square test of independence based on the information in the table. Choose the correct answer below.

A.

H0:

Age group and social networking site are independent of one another.

H1:

Age group and social networking site are not independent of one another.

B.

H0:

Age group and social networking site are independent of one another.

H1:

The age group affects the social networking site.

C.

H0:

Age group and social networking site are not independent of one another.

H1:

Age group and social networking site are independent of one another.

D.

H0:

Age group and social networking site are independent of one another.

H1:

The social networking site used affects the age group.

Calculate the chi-square test statistic. If necessary, combine age groups.

2=enter your response here

(Round to two decimal places as needed.)

Find the chi-square critical value, 2.

2=enter your response here

(Round to two decimal places as needed.)

Determine the result of the test. Choose the correct answer below.

A.

Reject H0. The test statistic does not fall into the rejection region.

B.

Reject

H0. The test statistic falls into the rejection region.

C.

Fail to reject

H0.The test statistic falls into the rejection region.

D.

Failtoreject

H0. The test statistic doesnotfall into the rejection region.

b. What conclusions can be made based on these results?

There is(sufficient, insufficient) evidence to indicate that

(age group and social networking site are not independent of each other,

The social networking site used affects the age group,

age group and social networking site are independent of each other,

the age group affects the social networking site used)

c. Determine the p-value using technology and interpret its meaning.

p-value=enter your response here

(Round to three decimal places as needed.)

Interpret the meaning of the p-value.

The p-value is the probability of observing a(test statistic, critical value) as extreme or more extreme than the one observed under the assumption that the (null hypothesis, alternative hypothesis) is true. A p-value less than the significance level means that the (critical value, test statistic) is (likely, unlikely) enough that the (null hypothesis, alternative hypothesis) should be rejected. For this test, the p-value is(greater than, less than) =0.025, so (reject, do not reject) the (null hypothesis, alternative hypothesis.) There is (insufficient, sufficient) evidence to indicate that

(age group and social networking site are not independent of each other,

The social networking site used affects the age group,

age group and social networking site are independent of each other,

the age group affects the social networking site used)

15. The accompanying table shows the market share for smartphone manufacturers in 2018. The table also shows the frequency of purchases of smartphones by brand for a random sample of customers during 2019. Complete parts a and b.

Brand	Market Share (%) 2018	Observed Frequency 2019
CompanyA	36.5	21
CompanyB	23.25	13
CompanyC	16.75	7
CompanyD	11	3
CompanyE	12.5	6
Total	100	50

a. Using =0.01, perform a chi-square test to determine if the observed frequencies in the table are consistent with the report. Identify the null and alternative hypotheses for a chi-square test of independence based on the information in the table. Choose the correct answer below.

A.

H0:

The observed frequencies in the table are consistent with the report.

H1:

The country affects the observed frequency of purchases of smartphones.

B.

H0:

The observed frequencies in the table are consistent with the report.

H1:

The observed frequencies in the table are not consistent with the report.

C.

H0:

The observed frequencies in the table are not consistent with the report.

H1:

The country affects the observed frequency of purchases of smartphones.

D.

H0:

The observed frequencies in the table are not consistent with the report.

H1:

The observed frequencies in the table are consistent with the report.

Find the chi-square test statistic.

2=enter your response here

(Type an integer or decimal rounded to two decimal places as needed.)

Using =0.01, find the chi-square critical value, 2.

2=enter your response here

(Type an integer or decimal rounded to two decimal places as needed.)

The observed frequencies in the table

(are consistent, are not consistent)

with the report because(K, df, X^2, X^2 over a)

<(K, df, X^2, X^2 over a)

Therefore,(reject, do not reject) the null hypothesis.

b. Determine the p-value using Excel and interpret its meaning.

p-value=enter your response here

(Round to three decimal places as needed.)

The p-value represents the probability of (observing a test statistic, having a population measure) 2, from observed frequencies that are consistent with the report with a value at least as extreme as the calculated value of 2 if the null hypothesis is(true, false) Since the p-value is(less, greater than) than alpha,(fail to reject, reject)H0. There is(sufficient, insufficient) evidence to conclude that the observed frequencies in the table are inconsistent with the report.

16. A particular weight-loss company claims that the average weight a person lost after two weeks on its program is 6 lb. The following data represent the weight loss of 36 randomly selected adults who have been on the program for two weeks. Negative values represent weight gains (oops!). These data can also be found in the accompanying table. Complete parts a and b

8	7	9	9
9	12	3	-2
6	10	3	-2
7	0	12	4
4	4	4	0
-5	4	3	11
5	7	9	-3
0	6	6	-1

a. Using =0.05, perform a chi-square test to determine if the weight loss after two weeks on this program follows a normal probability distribution when =6 and =2.

Identify the null and alternative hypotheses for a chi-square test of independence based on the information in the table. Choose the correct answer below.

A.

H0:

The observed frequencies in the table follow a Poisson probability distribution.

H1:

The observed frequencies in the table follow a normal probability distribution.

B.

H0:

The observed frequencies in the table follow a normal probability distribution.

H1:

The observed frequencies in the table follow a Poisson probability distribution.

C.

H0:

The observed frequencies in the table do not follow a normal probability distribution.

H1:

The observed frequencies in the table follow a normal probability distribution.

D.

H0:

The observed frequencies in the table follow a normal probability distribution.

H1:

The observed frequencies in the table do not follow a normal probability distribution.

Find the chi-square test statistic. Use

x4,

4

6

and

8

as the ranges so that they are divided at the mean and the mean1 standard deviation.

2=enter your response here

(Type an integer or decimal rounded to two decimal places as needed.)

Using =0.05, find the chi-square critical value, 2.

2=enter your response here

(Type an integer or decimal rounded to two decimal places as needed.)

The observed frequencies in the table (follow, do not follow) a (normal, poisson) probability distribution because (K, df, X^2, X^2 over a) >(K, df, X^2, X^2 over a) Therefore,(reject, do not reject) the null hypothesis.

b. Determine the p-value using Excel and interpret its meaning.

p-value=enter your response here

(Round to three decimal places as needed.)

The p-value represents the probability of

(observing a test statistic, having a population measure)2, for the weight loss after two weeks with a value at least as extreme as the calculated 2 if the null hypothesis is(True, False)

17. A real estate company that rents vacation properties in an ocean-side community. They believe that the accompanying table represents the probability distribution for the number of bedrooms for rental properties. The other accompanying table shows the number of bedrooms from a random sample of rental properties that the real estate company collected.

a. Using =0.025, does this sample provide enough evidence to support the real estate company's belief about the probability distribution?

b. Determine the p-value for the chi-square test statistic using Excel and interpret its meaning.

Bedrooms	2	3	4	5	6
Probability	0.14	0.29	0.30	0.17	0.10

Bedrooms	2	3	4	5	6
Frequency	6	11	24	8	1

a. What is the null hypothesis, H0?

A.

The distribution of the numbers of bedrooms is as believed.

B.

The mean number of bedrooms is as believed.

C.

The mean number of bedrooms is not as claimed.

D.

The distribution of motivations differs from the claimed distribution.

What is the alternative hypothesis, H1?

A.

The distribution of motivations differs from the claimed distribution.

B.

The distribution of the numbers of bedrooms is as believed.

C.

The mean number of bedrooms is as believed.

D.

The mean number of bedrooms is not as claimed.

Calculate the test statistic.

2=enter your response here

(Round to two decimal places as needed.)

Determine the critical value.

2=enter your response here

(Round to two decimal places as needed.)

Determine the proper conclusion to the test.

(Fail to reject, Reject)the null hypothesis. The sample(provides, does not provide) evidence to support the real estate company's belief about the probability distribution.

b. p-value=enter your response here

(Round to three decimal places as needed.)

The p-value represents the probability of(observing a test statistic, having a population measure) for vacation properties, 2, with a value at least as extreme as the calculated 2 if the null hypothesis is(false, true)