Question

A simple random sample of size nequals15 is drawn from a population that is normally distributed. The sample mean is found to be x overbarequals19.6 and the sample standard deviation is found to be sequals6.3. Determine if the population mean is different from 26 at the alpha equals 0.01 level of significance. Complete parts ​(a) through ​(d) below. ​(a) Determine the null and alternative hypotheses. Upper H 0​: ▼ sigma mu p ▼ equals greater than not equals less than 26 Upper H 1​: ▼ sigma p mu ▼ greater than less than not equals equals 26 ​(b) Calculate the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) ​(c) State the conclusion for the test. A. Reject Upper H 0 because the​ P-value is greater than the alphaequals0.01 level of significance. B. Do not reject Upper H 0 because the​ P-value is less than the alphaequals0.01 level of significance. C. Do not reject Upper H 0 because the​ P-value is greater than the alphaequals0.01 level of significance. D. Reject Upper H 0 because the​ P-value is less than the alphaequals0.01 level of significance. ​(d) State the conclusion in context of the problem. There ▼ is is not sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 26.

Answer 1

a)

null hypothesis:		μ	=	26
Alternate Hypothesis:		μ	≠	26

b) p value =0.001 ( please try 0.002 if this comes wrong due to rounding error)

c) D. Reject H 0 because the​ P-value is less than the alpha equals 0.01

There is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 26.