Question

Consider the following hypothesis test.

H_{0}: μ ≤ 12

H_{a}: μ > 12

A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.64.

(a)

Compute the value of the test statistic. (Round your answer to three decimal places.)

(b)

Use the *t* distribution table to compute a range for the
*p*-value.

*p*-value > 0.2000.100 < *p*-value <
0.200 0.050 < *p*-value <
0.1000.025 < *p*-value < 0.0500.010 <
*p*-value < 0.025*p*-value < 0.010

(c)

At α = 0.05, what is your conclusion?

Do not reject *H*_{0}. There is sufficient
evidence to conclude that μ > 12.Reject *H*_{0}.
There is insufficient evidence to conclude that μ >
12. Reject *H*_{0}. There is
sufficient evidence to conclude that μ > 12.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that μ > 12.

(d)

What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer to three decimal places.)

test statistic≤test statistic≥

What is your conclusion?

Do not reject *H*_{0}. There is sufficient
evidence to conclude that μ > 12.Reject *H*_{0}.
There is insufficient evidence to conclude that μ >
12. Reject *H*_{0}. There is
sufficient evidence to conclude that μ > 12.Do not reject
*H*_{0}. There is insufficient evidence to conclude
that μ > 12.

Answer #1

(a)

(b)

Using t table,

0.010 < *p*-value < 0.025

(c)

Reject *H*0. There is sufficient evidence to conclude
that μ > 12.

(d)

Reject *H*0. There is sufficient evidence to conclude
that μ > 12.

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