Question

A simple random sample of size nequals40 is drawn from a population. The sample mean is found to be 110.4?, and the sample standard deviation is found to be 23.3. Is the population mean greater than 100 at the alpha=0.01 level of? significance?

Determine the null and alternative hypotheses.

Compute the test statistic.

Determine the? P-value.

What is the result of the hypothesis? test?

Answer #1

H0: <= 100

Ha: > 100 (Right tailed )

Test statistics

t = - / S / sqrt(n)

= 110.4 - 100 / 23.3 / sqrt(40)

= **2.823**

Degrees of freedom df = n-1 = 40-1 = 39

p-value at 39 df for the test statistics t = 2.823 is
**0.0037**

Since p-value < 0.01 significance level, we have sufficient evidence to reject H0.

We conclude at 0.01 level that we have enough evidence to support the claim.

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