Question

# 2. Two ride-sharing companies, A and B, provide service for a certain city. A random sample...

2. Two ride-sharing companies, A and B, provide service for a certain city. A random sample of 52 trips made by Company A and a random sample of 52 trips made by Company B were selected, and the number of miles traveled for each trip was recorded. The difference between the sample means for the two companies
(A−B) was used to construct the 95 percent confidence interval (1.86,2.15).
Which of the following is a correct interpretation of the interval?
A. We are 95 percent confident that the difference in sample means for miles traveled by the two companies is between 1.86 miles and 2.15 miles.
B. We are 95 percent confident that the difference in population means for miles traveled by the two companies is between 1.86 miles and 2.15 miles.
C. The probability is 0.95 that the difference in sample means for miles traveled by the two companies is between 1.86 miles and 2.15 miles.
D. The probability is 0.95 that the difference in population means for miles traveled by the two companies is between 1.86 miles and 2.15 miles.
E. About 95 percent of the differences in miles traveled by the two companies are between 1.86 miles and 2.15 miles.
3. Two community service groups, J and K, each have less than 100 members. Members of both groups volunteer each month to participate in a community-wide recycling day. A study was conducted to investigate whether the mean number of days per year of participation was different for the two groups. A random sample of 45 members of group J and a random sample of 32 members of group K were selected. The number of recycling days each selected member participated in for the past 12 months was recorded, and the means for both groups were calculated. A two-sample t-test for a difference in means will be conducted. Which of the following conditions for inference have been met?

I. The data were collected using a random method.
II. Each sample size is less than 10 percent of the population size.
III. Eachsamplesizeislargeenoughtoassumenormalityofthesampling
distribution of the difference in sample means.
A. I only
B. II only
C. III only
D. I and III only E. I, II, and III

Solution

Q 2

First of all, confidence interval is a means of predicting or estimating the population parameter and not sample statistic. Sample statistic is used to arrive the confidence interval. Further, as the very name suggests, the confidence level represents how confident one can be about the interval estimate.

Q 3

Two-sample t-test is valid only if the Normality condition and the randomness of data are satisfied. But, even when the distribution of the base data is not known, tests involving means can be done with t-test if the sample size(s) are large enough, say 30 or more. In that case, by Central Limit Theorem, sample average follows Normal distribution.

DONE