Confidence Interval Practice PDF

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STAT 218: Confidence Interval Practice Fall 2018

_____________________________________________________________________________________________ 1. A recent study examined hearing loss data for 1,771 U.S. teenagers. In this sample, 333 were found to have some level of hearing loss. Your goal is to estimate the true long run proportion of all U.S teenagers who have some level of hearing loss.

a.

Find the observed statistic (also called the point estimate).

US teenagers who have some level of hearing loss

b.

Find the margin of error associated with the 95% confidence interval. (3 pts)

.0182

c.

Construct a 95% confidence interval for the true long run proportion of all U.S. teenagers who have some level of hearing loss. .1689,.2062

d.

Interpret the confidence interval in context. Can we test that the proportion of the population has hearing loss

Suppose we are interested in whether or 1 in 5 teens have hearing loss or not. e.

In symbols, state the correct hypotheses to test this claim. Ho: n= .20 Ha: n > .20

f.

Based on your confidence interval above, would you reject or fail to reject the null hypotheses? Why? I would fail to reject the null hypothesis because the confidence interval was between .1689 and .2062 and the null hypothesis was equal to .20

STAT 218: Confidence Interval Practice Fall 2018

_____________________________________________________________________________________________ 2. What is the average time of a four-man Olympic Bobsleigh team? In the 2014 Sochi Olympics, the 27 finalist teams averaged 3.41 minutes with a standard deviation of 0.42.

a.

Find the observed statistic (also called the point estimate).

The 27 teams

b.

Find the margin of error associated with the 95% confidence interval. (3 pts)

The margin of error is .0182

c.

Construct a 95% confidence interval for the true long run average time of a four-man Olympic Bobsleigh team. The confidence interval for the true long run proportion of all US teenagers who have some level of hearing losing is between .1698 and .2062

d.

Interpret the confidence interval in context.

We are testing if the 1/5 equals .2

Suppose we are interested in whether an Olympic Bobsleigh team is slower than 3.5 minutes. e.

In symbols, state the correct hypotheses to test this claim. Ho: p = .2 Ha: p...