Question

The salaries of a random sample of 50 major league baseball players for 2012 are 3.44 million dollars. Assuming the distribution of salaries for all major league baseball players is normally distributed with a standard deviation of $0.712 million, test the claim that the mean salary of major league baseball players is less than 4 million dollars. Use a significance level of 0.05. What is the test statistic?
What is the critical value?
What is the p-value?
What is the decision?

Answer 1

This is the left tailed test .

The null and alternative hypothesis is

H₀ : = 4

H_a : < 4

Test statistic = t

= ( - ) / s / n

= (3.44 - 4) / 0.712 / 50

Test statistic = -5.562

df = 49

Critical value = -1.677

P-value = 0.000

|Test statistics | > critical value

Reject the null hypothesis .