Question

A store takes a random sample of 16 sales. The average sale for the sample is $2310 with a standard deviation of $148. Assume that sales are distributed normally.

A. Test the hypothesis that the sample mean is different from $2100?

B. Would the conclusion in a change if alpha= .1?

C. Construct a 95% confidence interval for the population mean?   

Answer 1

a) The test statistic here is computed as:

Now as this is a two tailed test, the p-value for n-1 = 15 degrees of freedom is computed from t distribution tables as:

p = 2P( t₁₅ > 5.68) = approx. 0

As the p-value here is very very low, the test is significant and we can reject the null hypothesis here and conclude that the mean is significantly different from $2100.

b) As the p-value is lower than 0.1 too, the result would remain the same here too and the test is significant at this level of significance as well.

c) From t distribution tables, we get for 15 degrees of freedom that:

P( -2.131 < t₁₅ < 2.131 ) = 0.95

Therefore the confidence interval here is obtained as:

This is the required confidence interval here.