Question

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

Consider the following hypothesis test.

H_{0}: μ = 22 |

H_{a}: 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 =

State your conclusion.

Reject *H*_{0}. There is insufficient evidence to
conclude that μ ≠ 22.

Reject *H*_{0}. There is sufficient evidence to
conclude that μ ≠ 22.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that μ ≠ 22.

Do not reject *H*_{0}. 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 =

State your conclusion.

Reject *H*_{0}. There is insufficient evidence to
conclude that μ ≠ 22.

Reject *H*_{0}. There is sufficient evidence to
conclude that μ ≠ 22.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that μ ≠ 22.

Do not reject *H*_{0}. 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 =

State your conclusion.

Reject *H*_{0}. There is insufficient evidence to
conclude that μ ≠ 22.

Reject *H*_{0}. There is sufficient evidence to
conclude that μ ≠ 22.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that μ ≠ 22.

Do not reject *H*_{0}. There is insufficient
evidence to conclude that μ ≠ 22.

Answer #1

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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