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 wereM1 = 6.1.The ratings for women were M2 = 4.9. If the estimated standard error for the difference (sM1 − M2) is equal to 0.25, then consider the following.Find the confidence limits at an 80% CI for these two-independent samples. (Round your answers to two decimal places

Answer 1

Answer:

The 80% confidence interval for difference between two means is (0.85, 1.55).

Step-by-step explanation:

The (1 - α) % confidence interval for difference between two means is:

$CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2,(n_{1}+n_{2}-2)}\times SE_{\bar x_{1}-\bar x_{2}}$

Given:

$\bar x_{1}=M_{1}=6.1\\\bar x_{2}=M_{2}=4.9\\SE_{\bar x_{1}-\bar x_{2}}=0.25$

Confidence level = 80%

$t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.20/2, (5+5-2)}=t_{0.10,8}=1.397$

*Use a t-table for the critical value.

Compute the 80% confidence interval for difference between two means as follows:

$CI=(6.1-4.9)\pm 1.397\times 0.25\\=1.2\pm 0.34925\\=(0.85075, 1.54925)\\\approx(0.85, 1.55)$

Thus, the 80% confidence interval for difference between two means is (0.85, 1.55).