Using the t-distribution, it is found that the 80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is (2.85, 22.55).
We have the <u>standard deviations for the sample</u>, thus, the t-distribution is used. The interval is:
In which:
- M is the difference of the sample means.
- t is the critical value.
- s is the standard error of the sampling distribution.
The sample mean of mail-order purchases is of $94.50, while for internet sales is of $81.8, thus, the difference of the sample means is:
The standard error for <u>each sample</u> is the standard deviation of the sample divided by the square root of the sample size, thus:
The <em>standard error</em> of the sampling distribution is:
.
Then, using a t-distribution calculator or the t-table, the critical value for a <u>80% confidence interval</u> with 12 + 17 - 2 = <u>27 df</u> is of t = 1.314.
Then, the interval is:
The 80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is (2.85, 22.55).
A similar problem is given at brainly.com/question/24826023