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.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 30100
Alternative Hypothesis, Ha: μ ≠ 30100

Rejection Region
This is two tailed test, for α = 0.05 and df = 120
Critical value of t are -1.98 and 1.98.
Hence reject H0 if t < -1.98 or t > 1.98

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (30800 - 30100)/(4500/sqrt(121))
t = 1.711

P-value Approach
P-value = 0.0897
As P-value >= 0.05, fail to reject null hypothesis.