A researcher wants to know the proportion of teens (16 and 17-year-olds) who hav

Question

A researcher wants to know the proportion of teens (16 and 17-year-olds) who have texted while driving. What size sample should the researcher use if she wants an estimate within 2 percentage points of the true population proportion with 90% confidence if:

1.) Find the t-value such that the area under the t-distribution to the right of the t-value is 0.10, assuming 20 degrees of freedom (df). That is, find t10 with 20 degrees of freedom.

2.) Suppose for a simple random sample of 100 Americans age 15 or older, the mean time spent eating or drinking per day is 1.22 hours with a standard deviation of 0.65 hours. A histogram of time spent eating or drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.

Explanation / Answer

1) P(T > t) = 0.1

or, 1 - P(T < t) = 0.1

or, P(T < t) = 0.9

or, t = 1.325

2) According to the central limit theorem the sampling distribution of the mean approaches a normal distribution as the sample size (n) increases. The sampling distribution approaches normality regardless of the shape of the population distribution.

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