Consider the following sample data drawn independently from normally distributed

Question

Consider the following sample data drawn independently from normally distributed populations with equal population variances.

Sample 1

10.5

Sample 2

12.7

1 is the population mean for individuals with a CFA designation and 2 is the population mean of individuals with MBAs.

a. Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.

H0: 1 2 = 0; HA: 1 2 0

H0: 1 2 0; HA: 1 2 < 0

H0: 1 2 0; HA: 1 2 > 0

B1.Find the test Statistic

B2.Calculate the critical value at the 1% level of significance.

B3.Using the critical value approach, can we reject the null hypothesis at the 1% significance level?

C. Using the critical value approach, can we reject the null hypothesis at the 5% level?

Sample 1

10.5

Sample 2

12.7

11 9.3 10.8 11.9 7.3 12.5 12.5 11.4 10.6 9.7 9.8 10 7.2 12.6

Explanation / Answer

The statistical software output for this problem is:

Two sample T hypothesis test:
1 : Mean of Sample 1
2 : Mean of Sample 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 < 0
(with pooled variances)

Hypothesis test results:

Hence,

a) Hypotheses: H0: 1 2 0; HA: 1 2 < 0; Option B is correct.

b - 1) Test statistic = -1.592

b - 2) Critical value = -2.624

b - 3) No, since the value of the test statistic is not less than the critical value of -2.624.

Option D is correct.

c) No, since the value of the test statistic is not less than the critical value of -1.761.

Option A is correct.

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -1.3 0.81676081 14 -1.5916533 0.0669

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.