Question

Consider the following hypothesis test.

H_{0}: μ = 15 |

H_{a}: μ ≠ 15 |

A sample of 50 provided a sample mean of 14.11. The population standard deviation is 3.

(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.)

*p*-value =

(c)

At

*α* = 0.05,

state your conclusion.

Reject *H*_{0}. There is sufficient evidence to
conclude that *μ* ≠ 15.Reject *H*_{0}. There
is insufficient evidence to conclude that *μ* ≠
15. Do not reject*H*_{0}. There is sufficient evidence to conclude
that *μ* ≠ 15.Do not reject *H*_{0}. There is
insufficient evidence to conclude that *μ* ≠ 15.

(d)

State the critical values for the rejection rule. (Round your answers 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* ≠ 15.

Reject *H*_{0}. There is insufficient evidence to
conclude that *μ* ≠ 15.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that *μ* ≠ 15.

Do not reject *H*_{0}. There is insufficient
evidence to conclude that *μ* ≠ 15.

Answer #1

The population standard deviation is 3 is known therefore we use z-test

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