Question

ONE OF THE GIVEN ANSWERS FOR THE QUESTIONS ARE INCORRECT. FIND THE WRONG ANSWER AND CORRECT IT. THE BOLDED ANSWERS DO NOT NEED CORRECTING.

1. The major you choose in college can have an impact on your future in terms of income and quality of life. Some majors, such as petroleum engineering and pharmaceutical sciences, make more on average than other majors. A random sample of 22 petroleum engineering and pharmaceutical sciences graduates have a mean annual salary of $54,118 with a standard deviation of $1479. Given that the distribution is approximately normal, test the hypothesis that the mean annual salary for petroleum engineering and pharmaceutical sciences graduates is $53,000.

1. What is the critical value: +-2.080
2. Test statistic: 3.55
3. P-value: 0.0019
4. Decision: Reject the null because the test statistic is in the critical region and p-value is less than alpha.

2. The mean salary of a random sample of 50 major league baseball players for 2012 is $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.

1. What is the critical value: -1.676
2. Test statistic: -5.56
3. P-value: 1.34*10^-8
4. Decision: Reject the null because the test statistic is in the critical region and p-value is less than alpha.

Answer Choices:

1. 0.9990
2. -5.56
3. 0.9999  
4. 3.55
5. 0.0019
6. 2.68*10^-8
7. -1.645
8. +-1.721
9. +-2.080
10. -1.676  
11. 1.34*10^-8
12. Fail to reject the null because the test statistic is in the critical region and the p-value is greater than alpha.
13. Fail to reject the null because the test statistic is not in the critical region and the p-value is greater than alpha.
14. Reject the null because the test statistic is in the critical region and the p-value is greater than alpha.
15. Reject the null because the test statistic is not in the critical region and the p-value is less than alpha.
16. Reject the null because the test statistic is in the critical region and the p-value is less than alpha.
17. Fail to reject the null because the test statistic is not in the critical region and the p-value is less than alpha.

Answer 1

Note- All answers but (a) of second question i.e. critical value for baseball are correct.

2.

(a)

Sample size n = 50 (>30)

So, we can use normal distribution efficiently in place of t-distribution.

We know,

So, critical value is -1.64.

Note- I pointed out something wrong approach in your answer as follows.

• You considered t-distribution with degrees of freedom = 50-1 = 49 to calculate critical value and as you have taken the value -1.676.
• During calculation of p-value, you considered z-distribution as while .
• Such use of two different distributions in same probem is the mistake in your solution.