1.

Consider the observed frequencies to the right. Calculate the expected frequency for each observed frequency.

	Yes	No
A	20	26
B	10

Population	Expected Frequency of Yes	Expected Frequency of No
A	enter your response here	enter your response here
B	enter your response here	enter your response here

2. Consider the following observed frequencies. Calculate the expected frequency for each observed frequency.

Population	Yes	No
A	10	24
B	18	22
C	17	9

Calculate the expected frequency for each observed frequency.

Population	Expected Frequency of Yes	Expected Frequency of No
A	enter your response here	enter your response here
B	enter your response here	enter your response here
C	enter your response here	enter your response here

3. Using the accompanying data below, perform a chi-square test using =0.05 to determine if the proportion of "Yes" observations differs among Populations A, B, and C. (Right tail distribution)

Observed frequencies:

Population	Yes	No
A	11	21
B	17	27
C	18	6

Expected frequencies:

Population	Yes	No
A	14.72	17.28
B	20.24	23.76
C	11.04	12.96

What are the null and alternative hypotheses?

A.

H0:

pA=pB=pC

H1:

Not all p's are equal

B.

H0:

pApBpC

H1:

pA=pB=pC

C.

H0:

pA=pB=pC

H1:

pApBpC

D.

H0:

Not all p's are equal

H1:

pA=pB=pC

What is the test statistic?

2=enter your response here

(Round to two decimal places as needed.)

What is the critical value?

2=enter your response here

(Round to three decimal places as needed.)

What is the correct conclusion?

A.

Donotreject H0. There isnot enough evidence to conclude that the population proportions are different.

B.

Donotreject H0. There is enough evidence to conclude that the population proportions are different.

C.

Reject H0. There is enough evidence to conclude that the population proportions are different.

D.

Reject H0. There isnot enough evidence to conclude that the population proportions are different.

4. Suppose that a random sample of 100 men between the ages of 25 and 54 was selected and it was found that 81 were currently working. A similar sample of 100 women was selected and 69 were working. Complete parts a and b below.

a. Using =0.10, can it be concluded that the proportion of men in this age group who are working differs from the proportion of women who are working?

Determine the null and alternative hypotheses. Choose the correct answer below.

A.

H0:

pM>pW

H1:

pM

B.

H0:

pM=pW

H1:

pM>pW

C.

H0:

pM

H1:

pM>pW

D.

H0:

pM=pW

H1:

pMpW

E.

H0:

pM=pW

H1:

pM

F.

H0:

pMpW

H1:

pM=pW

What is the test statistic?

2=enter your response here

(Round to two decimal places as needed.)

What is the critical value?

2=enter your response here

(Round to two decimal places as needed.)

What is the correct conclusion?

(Do not reject, Reject) H0. There(is not, is) enough evidence to conclude that the proportion of men in this age group who are working differs from the proportion of women who are working.

b. Determine the p-value for the chi-square test statistic and interpret its meaning.What is the p-value?

p-value=enter your response here

(Round to three decimal places as needed.)

What does the p-value mean? Select the correct choice and fill in the answer box to complete your choice.(Round to one decimal places as needed.)

A.

There is a (enter your response here)%

margin of error for the accuracy of this data.

B.

Given a very large number of samples, there is a (enter your response here)%

chance of observing a sample with the given data.

C.

There is a( enter your response here)% chance of observing a test statistic value greater than the actual value of this test statistic if there is no difference in the working proportions.

D.

There is a (enter your response here)% chance of rejecting the null hypothesis when it should not be rejected.

5. A survey asked Democrats, Republicans, and Independent voters what the most important message is to send to Congress. The most popular response for all three groups was to "focus on the economy." The number of respondents, the messages they want sent, and their party affiliations are shown in the accompanying table. Complete parts a through c below.

Message	Democrat	Republican	Independent
Focus on economy	53	58	65
Other	96	119	57
Total	149	177	122

a. Using =0.05, perform a chi-square test to determine if the proportion of voters who responded "focus on the economy" differs among the three groups of voters.

What are the correct null and alternative hypotheses?

A.

H0:

pD=pR=pI

H1:

Not all p's are equal

B.

H0:

pDpRpI

H1:

pD=pR=pI

C.

H0:

Not all p's are equal

H1:

pD=pR=pI

D.

H0:

pD=pR=pI

H1:

pDpRpI

What is the test statistic?

2=enter your response here

(Round to two decimal places as needed.)

What is the critical value?

2=enter your response here

(Round to two decimal places as needed.)

What is the correct conclusion?

A.

Reject H0. There is enough evidence to conclude that the proportions of voters differ among the three groups of voters.

B.

Do not reject H0. There is enough evidence to conclude that the proportions of voters differ among the three groups of voters.

C.

Reject H0. There is not enough evidence to conclude that the proportions of voters differ among the three groups of voters.

D.

Do not reject H0. There is not enough evidence to conclude that the proportions of voters differ among the three groups of voters.

b. Interpret the meaning of the p-value.

What is the p-value?

p-value=enter your response here

(Round to three decimal places as needed.)What does the p-value mean? Select the correct choice and fill in the answer box to complete your choice.(Round to one decimal place as needed.)

A.

There is a (enter your response here)% chance of rejecting the null hypothesis when it should not be rejected.

B.

There is a (enter your response here)% margin of error for the accuracy of these data.

C.

Given a very large number of samples, there is a (enter your response here)% chance of observing a sample with the given data.

D.

There is a (enter your response here)% chance of observing a test statistic value greater than the actual test statistic value if there is no difference in the voter proportions.

c. How does party affiliation appear to affect the likelihood that a voter will choose the "focus on the economy" message to send to Congress?

A.

It appears that Independents are much more likely to want to send this message to Congress than Democrats or Republicans, who are fairly close in likelihood.

B.

It appears that Republicans are much less likely to want to send this message to Congress than Democrats or Independents, who are fairly close in likelihood.

C.

It appears that Democrats are much less likely to want to send this message to Congress than Republicans or Independents, who are fairly close in likelihood.

D.

Party affiliation does not appear to affect the likelihood that a voter will choose this message because the three proportions are all fairly close in likelihood or because the null hypothesis was not rejected.

6.

Consider the observed frequency distribution for the accompanying set of random variables. Perform a chi-square test using

=0.05

to determine if the observed frequencies follow the Poisson probability distribution when

=1.5.

RandomVariable,x	Frequency,fo
	0	17
	1	35
	2	29
	3	17
	4 and more	2
Total	100

What is the null hypothesis, H0?

A.

The random variable does not follow the Poisson distribution with

=1.5

B.

The random variable follows a normal distribution

C.

The random variable follows a uniform distribution.

D.

The random variable follows the Poisson distribution with

=1.5.

What is the alternate hypothesis, H1?

A.

The random variable follows the Poisson distribution with

=1.5.

B.

The random variable follows a uniform distribution.

C.

The random variable does not follow the Poisson distribution with

=1.5.

D.

The random variable follows a normal distribution.

Calculate the test statistic.

2=enter your response here

(Round to two decimal places as needed.)

Determine the p-value.

p-value=enter your response here

(Round to three decimal places as needed.)

State the appropriate conclusion.

(Do not reject, Reject) the null hypothesis because the p-value is (less than, greater than) . There is(sufficient, insufficient) evidence to conclude that the observed frequency distribution does not follow Poisson probability distribution.

7. Consider the observed frequency distribution for a set of grouped random variables available below. Perform a chi-square test using a =0.10 to determine if the observed frequencies follow the normal probability distribution with =99 and =21.

Random variable X	Frequency Fo
less than 78	9
78 to under 99	16
99 to under 120	19
120 and more	6
Total	50

State the appropriate null and alternative hypotheses. What is the null hypothesis?

A.

H0:

The mean number of the random variable is not equal to

99.

B.

H0:

The random variable does not follow the normal probability distribution.

C.

H0:

The mean number of the random variable is equal to

99.

D.

H0:

The random variable follows the normal probability distribution.

What is the alternative hypothesis?

A.

H1:

The random variable does not follow the normal probability distribution

B.

H1:

The mean number of the random variable is not equal to

99.

C.

H1:

The random variable follows the normal probability distribution.

D.

H1:

The mean number of the random variable is equal to

99.

Calculate the chi-square test statistic,2.

2=enter your response here

(Round to two decimal places as needed.)

Determine the p-value.

p-value=enter your response here

(Round to three decimal places as needed.)

State the appropriate conclusion.

(Do not reject, Reject) H0. There is (sufficient, insufficient) evidence to conclude that the random variable does not follow the normal probability distribution

8. The accompanying table shows the market share for automotive manufacturers in 2013. Also shown is the frequency of car purchases by manufacturer from a random sample of 210 customers in March of 2018. Use these data to complete parts a and b.

Manufacturer	Market Share 2013 (%)	Frequency 2018
A	19.4%	38
B	16.7%	31
C	14.2%	30
D	11.2%	30
E	11.1%	21
Other	27.4%	60
Total	100%	210

a. Using =0.05, perform a chi-square test to determine if the market share in the automotive industry has changed between 2013 and 2018. What is the null hypothesis,H0?

A.

The distribution of manufacturer's market shares is

38

manufacturer A,

31

manufacturer B,

30

manufacturer C,

30

manufacturer D,

21

manufacturer E, and

60

from other manufacturers.

B.

The distribution of manufacturer's market shares differs from the claimed or expected distribution.

C.

The distribution of manufacturer's market shares is

19.4%

manufacturer A,

16.7%

manufacturer B,

14.2%

manufacturer C,

11.2%

manufacturer D,

11.1%

manufacturer E, and

27.4%

from other manufacturers.

D.

The distribution of manufacturer's market shares follows the normal distribution.

What is the alternative hypothesis,

H1?

A.

The distribution of manufacturer's market shares differs from the claimed or expected distribution.

B.

The distribution of manufacturer's market shares is 20% manufacturer A, 20% manufacturer B, 20% manufacturer C, 20% manufacturer D, and 20% from other manufacturers.

C.

The distribution of manufacturer's market shares does not follow the normal distribution.

D.

The distribution of manufacturer's market shares is the same as the claimed or expected distribution.

The test statistic is

enter your response here.

(Round to two decimal places as needed.)

b. Determine the p-value for the chi-square test statistic using Excel and interpret its meaning.Identify a function that can be used in Excel to directly calculate the p-value (with no other calculations needed other than calculating the arguments of the function itself).

=T.DIST.2T(x,deg_freedom)

=NORM.S.DIST(z,cumulative)

=CHISQ.DIST.RT(x,deg_freedom)

=T.DIST.RT(x,deg_freedom)

=CHISQ.DIST(x,deg_freedom,cumulative))

Determine the p-value.

p-value=enter your response here

(Round to three decimal places as needed.)

Interpret the p-value.

The p-value is the probability of observing a value for the test statistic

(greater than, equal to, less than) the calculated test statistic, assuming

(the distribution of the variable differs from the normal distribution.)

(the distribution of the variable differs from the given distribution.)

(at least one expected frequency differs from 5.)

(the distribution of the variable is the normal distribution.)

(the expected frequencies are all equal to 5.)

(the distribution of the variable is the same as the given distribution.)

Draw a conclusion.

Because the p-value is (greater than, less than, equal to) =0.05, (fail to reject, reject)H0. At the 5% significance level, there (is, is not) enough evidence to conclude that the distribution of education levels(differs from, is the same as) the(normal distribution, uniform distribution, claimed or expected distribution.)

9. Recall that to construct a confidence interval for the mean when the population standard deviation is unknown, the population must follow the normal probability distribution. To test this condition, the following data show a random sample of weekly visits by patients to a chiropractic office. Complete parts a and b below.

72 90 109 123 122 121 119 129 117 72 85 81 70 83 74 92 89 88 87 86 100 91 113 110 101 102 107 111 107 110 102 128 128 108

a. Using =0.05, perform a chi-square test to determine if the number of patient visits per week follows the normal distribution. Note that x=100.8, and s=17.5.

State the appropriate null and alternative hypotheses. Choose the correct answer below.

A.

H0:

The number of weekly patient visits does not follow the normal distribution.

H1:

The number of weekly patient visits follows the normal distribution.

B.

H0:

The mean number of weekly patient visits is

100.8.

H1:

The mean number of weekly patient visits is less than

100.8.

C.

H0:

The mean number of weekly patient visits is

100.8.

H1:

The mean number of weekly patient visits is greater than

100.8.

D.

H0:

The number of weekly patient visits follows the normal distribution.

H1:

The number of weekly patient visits does not follow the normal distribution.

Use the following intervals to calculate the chi-square test statistic,

2.

Interval 1:			z		1.0
Interval 2:	1.0	<	z		0
Interval 3:	0	<	z		1.0
Interval 4:	1.0	<	z

The chi-square test statistic is

2=enter your response here.

(Round to two decimal places as needed.)

The chi-square critical value is

2=enter your response here.

(Round to three decimal places as needed.)

Draw the proper conclusion.

(Do not reject, Reject) the null hypothesis. There(is not, is) enough evidence to conclude that the number of weekly patient visits

(is not 100.8.

is 100.8.

is greater than 100.8.

follows the binomial distribution.

is less than 100.8.

follows the normal distribution.)

b. Determine the p-value and interpret its meaning.The p-value is

enter your response here.

(Round to three decimal places as needed.)

Interpret the p-value.

The p-value is the probability of observing a test statistic (equal to, less than, greater than) the part a statistic, assuming

(the mean number of weekly patient visits is less than 100.8.

the mean number of weekly patient visits is not 100.8.

the mean number of weekly patient visits is 100.8.

the distribution of the variable follows the normal distribution.

the distribution of the variable does not follow the normal distribution.

the mean number of weekly patient visits is greater than 100.8.)

10. The accompanying data shows the weekly purchases of printers at a particular electronic store. Using

=0.05, perform a chi-square test to determine if the number of printers sold per week follows a normal probability distribution. Note that x=11.3 and s=4.4.

8 16 12 18 11 15 4 8 4 4 15 6 16 16 9 12 18 12 13 5 9 9 9 8 17 8 9 15 7 19 10 4 8 12 7 15 11 14 14 13 11 12 8 17 20

State the appropriate null and alternative hypotheses. What is the null hypothesis?

A.

H0:

The mean number of weekly printers purchased is not

11.3.

B.

H0:

The mean number of weekly printers purchased is

11.3.

C.

H0:

The number of printers sold per week at the electronic store follows the normal probability distribution.

D.

H0:

The number of printers sold per week at the electronic store does not follow the normal probability distribution.

What is the alternative hypothesis?

A.

H1:

The mean number of weekly printers purchased is not

11.3.

B.

H1:

The mean number of weekly printers purchased is

11.3.

C.

H1:

The number of printers sold per week at the electronic store does not follow the normal probability distribution.

D.

H1:

The number of printers sold per week at the electronic store follows the normal probability distribution.

Use the intervals below to calculate the chi-square test statistic, 2.

Interval 1:			z		1.0
Interval 2:	1.0	<	z		0
Interval 3:	0	<	z		1.0
Interval 4:	1.0	<	z

2=enter your response here

(Round to two decimal places as needed.)

Determine the p-value.

p-value=enter your response here

(Round to three decimal places as needed.)

State the appropriate conclusion.

(Reject, Do not reject) H0. There(is not, is) enough evidence to conclude that the number of printers sold per week at the electronic store does not follow the normal probability distribution.