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Statistics

1. A study of 35 golfers showed that their average score on a particular course was 92. The standard deviation of the population is 5.
A. Find the best point estimate of the mean.
B. Find the 95% confidence interval of the mean score for all golfers.
C. Find the 95% confidence interval of the mean score if a sample of 60 golfers is used instead of a sample of 35.
D. Which interval is smaller? Explain why.

2. A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large plain pizza. How large should the sample be if she wishes to be accurate to within $0.5? A previous study showed that the standard deviation of the price was $0.26.

3. A sample of six college wrestlers had an average weight of 276 pounds with a sample standard deviation of 12 pounds.
A. Find the 90% confidence interval of the true mean weight of all college wrestlers.
B. If a coach claimed that the average weight of wrestlers on the team is 310, would the claim be believable?

4. It has been reported that 20.4% of incoming freshmen indicate that they will major in business or a related field. A random sample of 400 incoming college freshmen was asked their preference, and 95 replied that they were considering business as a major.
A. Estimate the true proportion of freshman business majors with 98% confidence.
B. Does your interval contain 20.4?

5. Nearly one half of Americans aged 25 to 29 are unmarried. How large a sample is necessary to estimate the true proportion of unmarried Americans in this age group within 21/2 percentage points within 90% confidence?

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