Note: Answer the Question(s) by Using the TI-30XA (or other approved) Calculator

Question

Note: Answer the Question(s) by Using the TI-30XA (or other approved) Calculator IMPORTANT: Make sure you carry all decimals until you reach your answer, then round to four decimals. 12 5 Consider the following data for two independent random samples taken from two normal populations with equal variances. Find 16 the 95% confidence interval for ? 1-u2. (See exercise 11 on page 449 of your textbook for a similar problem.) 18 20 21 Sample 1 23 Left Endpoint Right Endpoint 28 Click to Grade Your Work 31 Daily Problem ? EI m + 100% 100%

Explanation / Answer

Sample 1

Mean = 9

sample 2

Mean = 12

Pooled Variance
s2p = ((df1)(s21) + (df2)(s22)) / (df1 + df2) = 12.4 / 10 = 6.2

Standard Error
s(M1 - M2) = ?((s2p/n1) + (s2p/n2)) = ?((6.2/6) + (6.2/6)) = 1.44

Confidence Interval
?1 - ?2 = (M1 - M2) ± ts(M1 - M2) = 3 ± (2.23 * 1.44) = 3 ± 3.2

?1 - ?2 = (M1 - M2) = 3, 95% CI [-0.2, 6.2].

You can be 95% confident that the difference between your two population means (?1 - ?2) lies between -0.2 and 6.2.

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