Question

If the population average income for owners of Mamma Mia Pizza Shops is $30,100, does a special course on pizza store management given to a sample of 121 owners have any effect in increasing revenues. The average for those given the special course is $30,800, with a standard deviation of $4,500 across the sample of 121 owners. Test the hypothesis that the course has a significant effect using an alpha of .05, with a directional one-tail test.

Please explain how to find p value and what test should be used

Answer 1

Here we have population standard deviation is unknown and distribution of population is not given.

So we use t test for single population mean.

Null and alternative hypotheses

Ho : = 30100

Ha : > 30100

Test statistic

t = xbar - /(s/√n)

t = (30800-30100)/4500/√121

t = 1.71

p-value for right tailed test with t = 1.71 and degree of freedom = d.f= n -1 = 120

p-value = P( t > 1.71) d.f = 120

Using t table

p-value = 0.0449

Decision rule : if p-value < ( level of significance) we reject the null hypothesis otherwise we fail to reject the null hypothesis.

Our p-value = 0.0449 < 0.05

Decision : we reject the null hypothesis

There is sufficient evidence to support hypothesis that the course has a significant effect.