You may need to use the appropriate technology to answer this question. Consider the following hypothesis test. H0: ? ≥ 90 Ha: ? < 90 A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use ? = 0.01. (a) x = 88.5 Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is sufficient evidence to conclude that ? < 90.Do not reject H0. There is sufficient evidence to conclude that ? < 90. Do not reject H0. There is insufficient evidence to conclude that ? < 90.Reject H0. There is insufficient evidence to conclude that ? < 90. (b) x = 87 Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is sufficient evidence to conclude that ? < 90.Do not reject H0. There is sufficient evidence to conclude that ? < 90. Do not reject H0. There is insufficient evidence to conclude that ? < 90.Reject H0. There is insufficient evidence to conclude that ? < 90. (c) x = 85.5 Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is sufficient evidence to conclude that ? < 90.Do not reject H0. There is sufficient evidence to conclude that ? < 90. Do not reject H0. There is insufficient evidence to conclude that ? < 90.Reject H0. There is insufficient evidence to conclude that ? < 90. (d) x = 92 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. There is sufficient evidence to conclude that ? < 90.Do not reject H0. There is sufficient evidence to conclude that ? < 90. Do not reject H0. There is insufficient evidence to conclude that ? < 90.Reject H0. There is insufficient evidence to conclude that ? < 90.

Question

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

Consider the following hypothesis test.

H₀: ? ≥ 90

H_a: ? < 90

A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use

? = 0.01.

(a)

x = 88.5

Find the value of the test statistic.

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

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that ? < 90.Do not reject H₀. There is sufficient evidence to conclude that ? < 90. Do not reject H₀. There is insufficient evidence to conclude that ? < 90.Reject H₀. There is insufficient evidence to conclude that ? < 90.

(b)

x = 87

Find the value of the test statistic.

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

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that ? < 90.Do not reject H₀. There is sufficient evidence to conclude that ? < 90. Do not reject H₀. There is insufficient evidence to conclude that ? < 90.Reject H₀. There is insufficient evidence to conclude that ? < 90.

(c)

x = 85.5

Find the value of the test statistic.

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

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that ? < 90.Do not reject H₀. There is sufficient evidence to conclude that ? < 90. Do not reject H₀. There is insufficient evidence to conclude that ? < 90.Reject H₀. There is insufficient evidence to conclude that ? < 90.

(d)

x = 92

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. There is sufficient evidence to conclude that ? < 90.Do not reject H₀. There is sufficient evidence to conclude that ? < 90. Do not reject H₀. There is insufficient evidence to conclude that ? < 90.Reject H₀. There is insufficient evidence to conclude that ? < 90.