Question

in a random sample of ten people, the mean driving distance to work was 20.9 miles and the standard deviation was 5.8 miles. assume the population is normally distributed and use the t - distribution to find the margin of error and construct a 90% confidence interval for the population mean μ. interpret the results.
( type an integer or a decimal. do not round. )
a. with % confidence, it can be said that most driving distances to work (in miles) in the population are between the intervals endpoints.
b. it can be said that % of the population has a driving distance to work (in miles) that is between the intervals endpoints.
c. with % confidence, it can be said that the population mean driving distance to work (in miles) is between the intervals endpoints.
d. % of all random samples of ten people from the population will have a mean driving distance to work (in miles) that is between the intervals endpoints.

Explanation:

Step1: Recall Confidence Interval Interpretation

A confidence interval for a population mean (μ) is used to estimate the range within which the true population mean is likely to fall, with a certain level of confidence (here, 90%).

Step2: Analyze Each Option

• Option A: Talks about "most driving distances" (individual values), but confidence intervals for the mean are about the population mean, not individual values. Eliminate A.
• Option B: Claims a percentage of the population has distances in the interval. Confidence intervals don’t describe the proportion of the population in the interval (that’s a misinterpretation). Eliminate B.
• Option C: States that with 90% confidence, the population mean driving distance is between the interval’s endpoints. This matches the correct interpretation of a confidence interval for μ.
• Option D: Talks about sample means, but confidence intervals are about the population mean, not sample means’ distribution. Eliminate D.

Answer:

C. With 90% confidence, it can be said that the population mean driving distance to work (in miles) is between the interval’s endpoints.