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.

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