Question

Please process this excel

The following are summary statistics for a set of data. Number of samples = 18, sample average = 5.76, sample standard deviation = 0.493. At a 0.05 significance level is the population average less than 6? Show calculations and provide the proper statement with respect to the hypothesis and rejection or fail to reject. Which statistical distribution did you use to evaluate the test and why? Was this a one-tail test or a two-tail test?

Answer 1

Solution:

Given:

sample mean is = 5.76 and the Sample standard deviation is s = 0.493, and the sample size is n = 18.

Null and Alternative Hypotheses:

This corresponds to a left-tail test, for which a t-test for one mean, with unknown population standard deviation will be used.

Test statistic:

Formula:

The number of degrees of freedom are df = n-1 = 18-1=17

Rejection Region:
Given significance level = α = 0.05 and df = 17
So p-value = 0.0272 …Using excel formula, =TDIST(2.065,17,1)

Decision:

Since P-value < 0.05, reject H0.

Conclusion: Therefore, there is enough evidence to claim that the population mean μ is less than 6, at the 0.05 significance level.

Done