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Confidence Intervals and Sample Size for Juice Bottles

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1. The amounts (in ounces) of juice in eight randomly selected juice bottles are:

15.4 15.7 15.2 15.8 15.8 15.4 15.0 15.6

Assuming the population of amounts in juice bottles is known to be normally distributed, create a 95% confidence interval estimate for &#61549;, the mean amount of juice in all bottles.

You will be asked to identify x-bar, s, &#61537;, df, t, E and the confidence interval. (3 points each)

2. Previous studies have indicated the standard deviation of annual earnings for college students is \$850. How large a sample would need to be taken to estimate the mean for college students' annual earnings to within \$200 with 99% confidence? (4.5 points)

3. A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. How large a sample would she need to collect to estimate this proportion to within 5% with 95% accuracy? (4.5 points)