Question

A simple random sample of size nequals40 is drawn from a population. The sample mean is found to be 104.3​, and the sample standard deviation is found to be 23.5. Is the population mean greater than 100 at the alphaequals0.05 level of​ significance? Determine the null and alternative hypotheses. Upper H 0​: ▼ mu less than 100 mu equals 100 mu greater than 100 mu less than 104.3 mu equals 104.3 mu greater than 104.3 Upper H 1​: ▼ mu less than 100 mu equals 100 mu greater than 100 mu less than 104.3 mu equals 104.3 mu greater than 104.3 Compute the test statistic. ▼ z 0 t 0 equals nothing ​(Round to two decimal places as​ needed.) Determine the​ P-value. The​ P-value is nothing. ​(Round to three decimal places as​ needed.) What is the result of the hypothesis​ test? ▼ Reject Do not reject the null hypothesis because the​ P-value is ▼ less than greater than the level of significance. At the alphaequals0.05 level of​ significance, the population mean ▼ is is not ▼ less than 100. different from 100. greater than 100. less than 104.3. different from 104.3. greater than 104.3.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 100
Alternative Hypothesis, Ha: μ > 100

Rejection Region
This is right tailed test, for α = 0.05 and df = 39
Critical value of t is 1.685.
Hence reject H0 if t > 1.685

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (104.3 - 100)/(23.5/sqrt(40))
t = 1.16

P-value Approach
P-value = 0.127
As P-value >= 0.05, Do not reject null hypothesis.

At the alphaequals0.05 level of​ significance, the population mean is not greater than 100.