Consider the following hypothesis test.

H₀: 80

H_a: < 80

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 = 78.5

Find the value of the test statistic.

__________

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

p-value =

State your conclusion.

A)Do not reject H₀. There is sufficient evidence to conclude that < 80

B).Do not reject H₀. There is insufficient evidence to conclude that < 80.

C)Reject H₀. There is sufficient evidence to conclude that < 80.

D)Reject H₀. There is insufficient evidence to conclude that < 80.

(b)

x = 77

Find the value of the test statistic.

__________

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

p-value =

State your conclusion.

A)Do not reject H₀. There is sufficient evidence to conclude that < 80.

B)Do not reject H₀. There is insufficient evidence to conclude that < 80.

C) Reject H₀. There is sufficient evidence to conclude that < 80.

D)Reject H₀. There is insufficient evidence to conclude that < 80.

(c)

x = 75.5

Find the value of the test statistic.

_________

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

p-value =

State your conclusion.

A)Do not reject H₀. There is sufficient evidence to conclude that < 80.

B)Do not reject H₀. There is insufficient evidence to conclude that < 80.

C)Reject H₀. There is sufficient evidence to conclude that < 80.

D)Reject H₀. There is insufficient evidence to conclude that < 80.

(d)

x = 80.5

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.

A)Do not reject H₀. There is sufficient evidence to conclude that < 80.

B)Do not reject H₀. There is insufficient evidence to conclude that < 80.

C)Reject H₀. There is sufficient evidence to conclude that < 80.

D)Reject H₀. There is insufficient evidence to conclude that < 80.