Question

Consider the following hypothesis test. Hoius 12 H: > 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.25. (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. O p-value > 0.200 O 0.100 < p-value < 0.200 O 0.050 < p-value < 0.100 O 0.025 < p-value < 0.050 O 0.010 < p-value < 0.025 O p-value < 0.010 (c) At a = 0.05, what is your conclusion? Reject Ho. There is insufficient evidence to conclude that u > 12. Reject Ho. There is sufficient evidence to conclude that u > 12. O Do not reject Ho. There is insufficient evidence to conclude that u > 12. O Do not reject Ho. There is sufficient evidence to conclude that u > 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 statistics test statistic > What is your conclusion? Reject Ho. There is insufficient evidence to conclude that u > 12. Reject Ho. There is sufficient evidence to conclude that u > 12. Do not reject Ho. There is insufficient evidence to conclude that u > 12. Do not reject Ho. There is sufficient evidence to conclude that u > 12.

Answer 1

a)

The test statistic is given by:

$t=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{14-12}{\frac{4.25}{\sqrt{25}}}=2.353$

b)

Degrees of freedom = n-1 = 25-1 = 24

Using the tables, the test statistic 2.353 for 24 df, lies between the values 0.01 and 0.025.

Hence 5th option.

c)

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0.

Reject H0. There is sufficient evidence to conclude that .

μΣ 12

Hence 2nd option.

d)

Critical value = $t_{n-1}(\alpha)=t_{25-1}(0.05)=t_{24}(0.05)=1.711$

Rejection region: Test statistic $\geq$ 1.711

NONE for the other tail.

Since the test statistic value lies is greater than the critical value, so we have sufficient evidence to reject H0.

Reject H0. There is sufficient evidence to conclude that .

μΣ 12

Hence 2nd option.