ifference between Means Using Two Independent Samples 3 E X ERCISE S 10.47 The a

Question

ifference between Means Using Two Independent Samples 3 E X ERCISE S 10.47 The article "Car rental prices can change in a heartbeat" (USA Today, March 14, 2007) reported that rates for car rentals can change many times during a day. The national average rate for the January-March quarter of 2007 was $52.71, yet in some cities, car rentals can cost more than $100 a day. A similar study of two major cities found the following results: City Bostolk City New York City n Average Daily Rate Standard Deviation 10 16 95.94 127.75 7.50 15.83 Set a 95% confidence interval on the difference in average daily rates between the two major East Coast cities of Boston and New York City. Assume normality for the sampled populations and that the samples were selected randomly 10.48 Women on average have 8 more pairs of shoes than men, according to a USA Today Snapshot titled "Who owns more shoes?" (July 8, 2009). A recent study at a community college gave the following results:

Explanation / Answer

The formula for estimation is:

1 - 2 = (M1 - M2) ± ts(M1 - M2)

where:

M1 & M2 = sample means
t = t statistic determined by confidence level
s(M1 - M2) = standard error = ((s2p/n1) + (s2p/n2))

Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 306.84 / 24 = 12.78

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((12.78/10) + (12.78/16)) = 1.44

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 31.81 ± (2.06 * 1.44) = 31.81 ± 2.9748

1 - 2 = (M1 - M2) = 31.81,

95% CI [28.8352, 34.7848].

You can be 95% confident that the difference between your two population means (1 - 2) lies between 28.8352 and 34.7848.

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