Question

# You may need to use the appropriate appendix table or technology to answer this question. Consider...

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

Consider the following hypothesis test.

 H0: μ = 22 Ha: μ ≠ 22

A sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.01.

(Round your test statistics to two decimal places and your p-values to four decimal places.)

(a) x = 24

Find the value of the test statistic.

Find the p-value.

p-value =

Reject H0. There is insufficient evidence to conclude that μ ≠ 22.

Reject H0. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H0. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 22.

(b) x = 25.2

Find the value of the test statistic.

Find the p-value.

p-value =

Reject H0. There is insufficient evidence to conclude that μ ≠ 22.

Reject H0. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H0. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 22.

(c) x = 21

Find the value of the test statistic.

Find the p-value.

p-value =

Reject H0. There is insufficient evidence to conclude that μ ≠ 22.

Reject H0. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H0. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 22.

a)

z = (x - mean)/(sigma/sqrt(n))
= (24 - 22)/(10/sqrt(75))
= 1.7321

p value = 0.0833

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 22.

b)

z = (x - mean)/(sigma/sqrt(n))
= (25.2 - 22)/(10/sqrt(75))
= 2.7713

p value = 0.0056

Reject H0. There is sufficient evidence to conclude that μ ≠ 22.

c)

z = (x - mean)/(sigma/sqrt(n))
= (21 - 22)/(10/sqrt(75))
= -0.8660

p value = .3865

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 22.

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