Question

A researcher claims that high-school students exercise an average (mean) of 8 hours per week. (You think that the number is actually higher.) From a sample of 40 students, you find a mean of 9 hours with a sample standard deviation of 1 hour. Conduct a hypothesis test using a 5% significance level.

a) What are the null and alternative hypotheses?

b) What is the test statistic?

c) What is the p-value?

d) Do your reject the null hypothesis? Explain your answer.

Answer 1

given data are:-

sample mean () = 9

sample sd (s) = 1

sample size (n) = 40

here,as the sample sd is known ,we will do 1 sample t test for mean.

a).hypothesis:-

b).the test statistic be:-

c). df = (n-1) = (40-1)= 39

p value = 0.0000

[ in any blank cell of excel type =T.DIST.RT(6.325,39) press enter]

d).decision:-

p value = 0.0000 < 0.05 (alpha)

so, we reject the null hypothesis.

conclusion:-

there is not sufficient evidence, to support the claim that high-school students exercise an average of 8 hours per week at 0.05 level of significance.

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