Question

To save money, a local charity organization wants to target its mailing requests for donations to individuals who are most supportive of its cause. They ask a sample of 5 men and 5 women to rate the importance of their cause on a scale from 1 (not important at all) to 7 (very important). The ratings for men were M1 = 6.3. The ratings for women were M2 = 5.2. If the estimated standard error for the difference (sM1 − M2) is equal to 0.25, then consider the following.

(a) Find the confidence limits at an 80% CI for these two-independent samples. (Round your answers to two decimal places.)

(b) Can we conclude that men or women are more supportive to their cause? Explain.

Yes, the lower and upper limits of the confidence interval are positive, indicating that mean ratings of importance are higher for the population of men compared to women.

Yes, the lower and upper limits of the confidence interval are negative, indicating that mean ratings of importance are higher for the population of women compared to men.

No, the lower and upper limits of the confidence interval contain zero, indicating that mean ratings of importance may not be higher for the population of men or women.

No, the lower and upper limits of the confidence interval are negative, indicating that mean ratings of importance may not be higher for the population of men or women.

Answer 1

Ans:

a)

df=5+5-2=8

critical t value=tinv(0.2,8)=1.397

80% Confidence interval for difference

=(6.3-5.2)+/-1.397*0.25

=1.1+/-0.35

=(0.75, 1.45)

b)

Yes, the lower and upper limits of the confidence interval are positive, indicating that mean ratings of importance are higher for the population of men compared to women.