Question

# You may need to use the appropriate technology to answer this question. Consider the following hypothesis...

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

Consider the following hypothesis test.

H0: μ ≥ 40

Ha: 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.)

p-value =

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.)

p-value =

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.

p-value =

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.

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

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

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

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

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