1) You may need to use the appropriate appendix table or technology to answer this question.Consider the following hypothesis test.

H₀: 20

H_a: < 20

A sample of 50 provided a sample mean of 19.1. The population standard deviation is 2.

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

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

(c)Using = 0.05, state your conclusion.

Reject H₀. There is sufficient evidence to conclude that < 20.

Reject H₀. There is insufficient evidence to conclude that < 20.

Do not reject H₀. There is sufficient evidence to conclude that < 20.

Do not reject H₀. There is insufficient evidence to conclude that < 20.

(d)State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic------------------

test statistic------------------

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that < 20.

Reject H₀. There is insufficient evidence to conclude that < 20.

Do not reject H₀. There is sufficient evidence to conclude that < 20.

Do not reject H₀. There is insufficient evidence to conclude that < 20.

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2)

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

Insure.com reports that the mean annual premium for automobile insurance in the United States was $1,365 in 2018. Being from Pennsylvania, you believe automobile insurance is cheaper there, and you wish to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,276 with a standard deviation of

s = $165.(Use = 0.05.)

(a)Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.

H₀: = 1,365

H_a: 1,365

H₀: < 1,365

H_a: 1,365

H₀: 1,365

H_a: < 1,365

H₀: 1,365

H_a: > 1,365

H₀: > 1,365

H_a: 1,365

(b)What is a point estimate (in dollars) of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)$ -----------------

(c)Find the value of the test statistic. (Round your answer to three decimal places.)What is the p-value? (Round your answer to four decimal places.)

p-value = ---------------

(d)At = 0.05, test for a significant difference. What is your conclusion?

Do not reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Do not reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

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3)

You may need to use the appropriate appendix table or technology to answer this question.Vegans are much less common in the United States than in the rest of the world. Suppose in a 2018 survey of 12,000 people in the United States, VeganBits found 36 who are vegans.

(a)Develop a point estimate of the proportion of people in the United States who are vegans. ----------

(b)Set up a hypothesis test so that the rejection of H₀ will allow you to conclude that the proportion of people in the United States who are vegans exceeds 0.002. (Enter != for as needed.)

H₀:---------------

H_a:-----------

(c)Conduct your hypothesis test using = 0.05.

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 = --------------

State your conclusion.

Reject H₀. We can conclude that the proportion of people in the United States who are vegans exceeds 0.002.

Reject H₀. We cannot conclude that the proportion of people in the United States who are vegans exceeds 0.002.

Do not reject H₀. We can conclude that the proportion of people in the United States who are vegans exceeds 0.002.

Do not reject H₀. We cannot conclude that the proportion of people in the United States who are vegans exceeds 0.002.

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