Question

A study was conducted to determine if the salaries of the professors from two neighbouring universities were

equal. A sample of 20 professors from each university was randomly selected. The mean from the first university
was $109,100 with a population standard deviation of $2300. The mean from the second university was $110,500
with a population standard deviation of $2100. Assume that the distribution of professor salaries, at both
universities, are approximately normally distributed. Level of significance = 0.05.

Use the four-step P-value approach and test the claim that the salaries from both universities are equal.

Answer 1

After calculating values from test statics we come to know that value of if null hypothesis is true then it will rejected

As critical values of z is ±1.96 after apply the test statics formula , we get the value of z that is - 4.50 As we consider the equation that

H₀ > z

Apply test statistic we fine the true value . So there is sufficient evidence to reject the claim.

Explanation:

critical values z₀ = ±1.96; standardized test statistic z ≅ -4.50;

reject H₀

There is sufficient evidence to reject the claim.