Question

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Consider the following hypothesis test.

H₀: μ ≥ 40

H_a: μ < 40

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 = 39 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.

Do not reject H₀. There is sufficient evidence to conclude that μ < 40.Reject H₀. There is insufficient evidence to conclude that μ < 40.    Reject H₀. There is sufficient evidence to conclude that μ < 40.Do not reject H₀. There is insufficient evidence to conclude that μ < 40.

(b)

x = 38 and s = 4.6

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.

Do not reject H₀. There is sufficient evidence to conclude that μ < 40.Reject H₀. There is insufficient evidence to conclude that μ < 40.    Reject H₀. There is sufficient evidence to conclude that μ < 40.Do not reject H₀. There is insufficient evidence to conclude that μ < 40.

(c)

x = 41 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.

Do not reject H₀. There is sufficient evidence to conclude that μ < 40.Reject H₀. There is insufficient evidence to conclude that μ < 40.    Reject H₀. There is sufficient evidence to conclude that μ < 40.Do not reject H₀. There is insufficient evidence to conclude that μ < 40.

Answer 1

Null and Alternative hypothesis:

Ho : µ ≥ 40

H1 : µ < 40

n = 36

α = 0.01

(a)

x = 39 and s = 5.3

Test statistic:

t = (x̅- µ)/(s/√n) = (39 - 40)/(5.3/√36) = -1.132

df = n-1 = 35

p-value = T.DIST(-1.1321, 35, 1) = 0.1326

State your conclusion.

Do not reject H₀. There is insufficient evidence to conclude that μ < 40.

(b)

x = 38 and s = 4.6

Test statistic:

t = (x̅- µ)/(s/√n) = (38 - 40)/(4.6/√36) = -2.609

df = n-1 = 35

p-value = T.DIST(-2.6087, 35, 1) = 0.0066

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ < 40.

(c)

x = 41 and s = 6.0

Test statistic:

t = (x̅- µ)/(s/√n) = (41 - 40)/(6/√36) = 1.000

df = n-1 = 35

p-value = T.DIST(1, 35, 1) = 0.8379

State your conclusion.

Do not reject H₀. There is insufficient evidence to conclude that μ < 40.