Consider the following hypothesis test:

Ho:µ=15

Ha:µ not equal to 15

A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3.

a. compute the value of the test statistic.

b.What is the p-value.

c. At a=.05 what is your conclusion?

d. what is the rejection rule using the critical value? what is your conclusion?

Worked solution:

We’re asked to calculate a test statistic. Note carefully that I am going to use the t distribution below----theoretically the normal distribution would work because n > 30, but I am super-careful and always use the t distribution for this.

Recall that we get the test statistic from

So now use Excel: =tdist(2.005,49,2)= 0.0505

degrees of freedom is n-1 = 50 -1 =49

tails is 2 ----look at the hypothesis

The p value is 0.0505. We are asked to test at 95% (meaning alpha = 0.05), so here p NOT smaller than or equal to alpha because 0.0505 > 0.05. Conclusion is fail to reject null hypothesis.

Note: this is very borderline case. A bit of rounding off the other way.....might have been a different conclusion.

The last part of the question asks about using the critical value. In my class I teach you ONLY the p value, so don’t worry about this part of the question.

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