Question

A simple random sample of size n 15 is drawn from a population that is normally distributed. The sample mean is found to be x 24.4 and the sample standard deviation is found to be s 6.3. Determine if the population mean is different from 26 at the 0.01 level of significance. Complete parts (a) through (d) below. (a) Determine the null and alternative hypotheses. ЕЕ (b) Calculate the P-value P.value Round to three decimal places as needed.) (c) State the conclusion for the test. O A. Do not reject HO because the P-value is less than the a-o 01 level of significance O B. Do not reject H0 because the P-value is greater than the α: 0.01 level of significance 0 C. Reject H0 because the P-value is less than the ":0 01 level of significance O D. Reject H0 because the P-value is greater than the α : 0.01 level of significance. (d) State the conclusion in context of the problenm There sufficient evidence at tea0.01 level of significance to conclude that the population mean is different from 26.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 26

H_a : $\mu$   $\neq$ 26

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (24.4 - 26) / 6.3 / $\sqrt$ 15

Test statistic = -0.98

df = 14

P-value = 0.3437

$\alpha$ = 0.01

P-value > $\alpha$

Do not reject H0 because the p-value is greater than the $\alpha$ = 0.01 level of significance .

There is not sufficient evidence at the 0.01 level of significance to conclude that the population mean is different from 26 .