Question

4. Are biomedical engineering salaries in Miami less than those in Minnesota? Salary data show that staff biomedical engineers in Miami earn less than those in Minnesota. Suppose that in a follow-up study of 35 staff engineers in Miami and 45 staff engineers in Minnesota you obtain the following results: Miami Minnesota n1 = 35 n2 = 45 1 = $64, 150 1 = $65, 450 s1 = $2000 s2 = 2500 a. Formulate a hypothesis statement so that if the null hypothesis is rejected, we can conclude that Miami biomedical engineering salaries are significantly lower than those in Minnesota. b. The standard deviations for both populations can be assumed equal, write out the statistic you would use. c. What would be your decision rule? (Use α = 0.05) d. What is the value of your statistic? e. What is your p-value? f. What is your conclusion?

(SHOW WORK)

Answer 1

a)

The Null and Alternative Hypotheses

where, is the mean salary in Miami and   is the mean salary in Minnesota.

The null hypothesis is defined as there is no difference in mean salary between Miami and Minnesota and the alternative hypothesis tests the claim that mean salary in Miami is less than in Minnesota.

b)

Since the population standard deviation is not know, the t statistic will be used to compare the mean salaries hence the Two sample t test is used to compare the means assuming equal variance.

c)

The t statistic is used to compare the two population means and the significance level for the test is

The decision rules state the conditions that if,

,

d)

The t statistic is obtained using the formula,

e)

The P-value for the t statistic is obtained from t distribution table for degree of freedom = n1+n2-2=78

f)

The corresponding P-value is 0.007 which is less than 0.05 at the 5% significance level for the one sided alternative hypothesis. Hence, it can be concluded that the null hypothesis is rejected.

Now we can conclude that there is significantly less salary in Miami compare to ​​​​​​​Minnesota.