Question

Consider the following hypothesis test.

H_{0}: μ ≤ 25 |

H_{a}: μ > 25 |

A sample of 40 provided a sample mean of 26.2. The population standard deviation is 6.

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

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

(c)At *α* = 0.01, state your conclusion.

Reject *H*_{0}. There is sufficient evidence to
conclude that *μ* > 25.

Reject *H*_{0}. There is insufficient evidence to
conclude that *μ* >
25.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that *μ* > 25.

Do not reject *H*_{0}. There is insufficient
evidence to conclude that *μ* > 25.

(d) State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic ≤

test statistic ≥

State your conclusion.

Reject *H*_{0}. There is sufficient evidence to
conclude that *μ* > 25.

Reject *H*_{0}. There is insufficient evidence to
conclude that *μ* >
25.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that *μ* > 25.

Do not reject *H*_{0}. There is insufficient
evidence to conclude that *μ* > 25.

Answer #1

a)

Test statistics

z = ( - ) / ( / sqrt(n) )

= (26.2 - 25) / (6 / sqrt(40) )

= **1.26**

b)

p-value = P(Z > z)

= P(Z > 1.26)

= **0.1038**

c)

Since p-value > 0.01 level, Fail to reject H0.

Do not reject H_{0}. There is insufficient evidence to
conclude that
> 25.

d)

z critical value at 001 level = 2.33

Rejection rule = Reject H0 if test statistics 2.33

Conclusion - Do not reject H_{0}. There is insufficient
evidence to conclude that
> 25.

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