Question

construct the 98% confidence interval for the difference $mu_1-mu_2$ when $\overline{x_1}=480.44$, $\overline{x_2}=320.76$, $s_1 = 42.36$, $s_2=25.76$, $n_1=14$, and $n_2=17$. use the ti - 84 plus calculator and round the answers to two decimal places.
a 98% confidence interval for the difference in the population means is $

Explanation:

Step1: Calculate the difference in sample means

The difference in sample means is \(\bar{x}_1-\bar{x}_2 = 480.44 - 320.76=159.68\)

Step2: Use the TI - 84 Plus calculator

1. Press STAT
2. Arrow over to TESTS
3. Arrow down to 2 - SampTInt (since the population standard deviations are unknown)
4. Enter the following values:

• \(\bar{x}_1 = 480.44\), \(s_1 = 42.36\), \(n_1=14\)
• \(\bar{x}_2 = 320.76\), \(s_2 = 25.76\), \(n_2 = 17\)
• C - Level=0.98
• Pooled: No (since we have no reason to assume equal variances)

1. Press Calculate

The calculator will give the confidence interval.

Answer:

\(140.57<\mu_1 - \mu_2<178.79\)