Question

Consider the following hypothesis test.

H₀: μ ≥ 55

H_a: μ <  55

A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use

α = 0.01.

(a)

x = 54 and s = 5.3

Find the value of the test statistic. (Round your answer to three decimal places.)

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

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that μ < 55.Do not reject H₀. There is sufficient evidence to conclude that μ < 55.     Reject H₀. There is sufficient evidence to conclude that μ < 55.Do not reject H₀. There is insufficient evidence to conclude that μ < 55.

(b)

x = 53 and s = 4.5

Find the value of the test statistic. (Round your answer to three decimal places.)

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

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that μ < 55.Do not reject H₀. There is sufficient evidence to conclude that μ < 55.     Reject H₀. There is sufficient evidence to conclude that μ < 55.Do not reject H₀. There is insufficient evidence to conclude that μ < 55.

(c)

x = 56 and s = 6.0

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 insufficient evidence to conclude that μ < 55.Do not reject H₀. There is sufficient evidence to conclude that μ < 55.     Reject H₀. There is sufficient evidence to conclude that μ < 55.Do not reject H₀. There is insufficient evidence to conclude that μ < 55.

Answer 1