1. A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.5 seconds. A random sample 21 of sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.11 seconds. At a = 0.05 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

(a) Identify the claim and state H0 and Ha

H0: (1)__________ (2)__________ 

Ha: (3)__________ (4)__________

(Type integers or decimals. Do not round.)

The claim is the (5)__________ hypothesis.

(b) Use technology to find the P-value. Find the standardized test statistic, t.

t =__________

(Round to two decimal places as needed.)

Obtain the P-value.

P =__________

(Round to three decimal places as needed.)

(c) Decide whether to reject or fail to reject the null hypothesis.

(6)__________ H0 because the P-value (7)__________ greater than α

(d) Interpret the decision in the context of the original claim.

There (8)__________ enough evidence at the__________ % level of significance to (9)__________ the claim that the mean minimum time it takes for a sedan to travel a quarter mile is (10)__________ seconds.

(Type integers or decimals. Do not round.)

2. For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, a is the level of significance,  is the sample proportion, and n is the sample size. If it can be used, test the claim.

If a normal sampling distribution can be used, identify the hypotheses for testing the claim. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

If a normal sampling distribution can be used, identify the critical value(s) for this test. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. z0 =__________

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

B. A normal sampling distribution cannot be used.

If a normal sampling distribution can be used, identify the rejection region(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.

A. The rejection region is z <_________ .

(Round to two decimal places as needed.)

B. The rejection region is z >_________ .

(Round to two decimal places as needed.)

C. The rejection regions are z < and z >_________ .

(Round to two decimal places as needed.)

D. The rejection region is < z <_________ .

(Round to two decimal places as needed.)

E. A normal sampling distribution cannot be used.

If a normal sampling distribution can be used, identify standardized test statistic z. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. z =__________

(Round to two decimal places as needed.)

B. A normal sampling distribution cannot be used.

If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision. Choose the correct answer below.

A. Fail to reject the null hypothesis. There is not enough evidence to reject the claim.

B. Reject the null hypothesis. There is not enough evidence to reject the claim.

C. Reject the null hypothesis. There is enough evidence to reject the claim.

D. Fail to reject the null hypothesis. There is enough evidence to reject the claim.

E. A normal sampling distribution cannot be used.

3. A research center claims that at least 25% of adults in a certain country think that their taxes will be audited. In a random sample of 1100 adults in that country in a recent year, 20% say they are concerned that their taxes will be audited. At a=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below.

(a) Identify the claim and state H0 and Ha.

Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.)

A. The percentage of adults in the country who think that their taxes will be audited is not______ %.

B. ______ % of adults in the country think that their taxes will be audited.

C. At least ______ % of adults in the country think that their taxes will be audited.

D. Less than______  % of adults in the country think that their taxes will be audited.

Let p be the population proportion of successes, where a success is an adult in the country who thinks that their taxes will be audited. State H0 and Ha. Select the correct choice below and fill in the answer boxes to complete your choice.(Round to two decimal places as needed.)

(b) Find the critical value(s) and identify the rejection region(s).

Identify the critical value(s) for this test.

z0 =________

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

Identify the rejection region(s). Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)

A. The rejection regions are z <_____ and z >_____ .

B. The rejection region is_____ < z <_____ .

C. The rejection region is z <_____ .

D. The rejection region is z >_____ .

(c) Find the standardized test statistic z.

z =________

(Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim.

(1)______ the null hypothesis. There (2)______ enough evidence to (3)______ the center's claim.

(1) Reject

Fail to reject

(2) is

is not

(3) reject

support

4. A research center claims that 27% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 31% say that they would travel into space on a commercial flight if they could afford it. At a=0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below.

(a) Identify the claim and state H0 and Ha.

Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.)

A. At least _______% of adults in the country would travel into space on a commercial flight if they could afford it.

B.  _______% of adults in the country would travel into space on a commercial flight if they could afford it.

C. No more than _______ % of adults in the country would travel into space on a commercial flight if they could afford it.

D. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not _______ %. 

Let p be the population proportion of successes, where a success is an adult in the country who would travel into space on a commercial flight if they could afford it. State H0 and Ha. Select the correct choice below and fill in the answer boxes to complete your choice.

(b) Use technology to find the P-value.

Identify the standardized test statistic.

z =__________

(Round to two decimal places as needed.)

Identify the P-value.

P =__________

(Round to three decimal places as needed.)

(c) Decide whether to reject or fail to reject the null hypothesis and (d) interpret the decision in the context of the original claim.

(1)__________ the null hypothesis. There (2)__________ enough evidence to (3)__________ the research center's claim.

(1) Reject

Fail to reject 

(2) is

not is

(3) support

reject