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# Solutions to Various Statistics Problems

1. Each day of the year a large sample of cellular phone calls is selected and a 95% confidence interval is calculated for the mean length of all cellular phone calls on that day. Of these 365 confidence intervals, one for each day of the year, approximately how many will cover their respective population means? Explain your reasoning

2. NOTE: x-; represents x bar (sample mean)
A forester measures 100 needles off a pine tree and finds x-; = 3.1 centimeters and s=0.7 centimeter. She reports that a 95% confidence interval for the mean needle length is
3.1-1.96(0.7/sqrt(100)) to 3.1 + 1.96(0.7/sqrt(100)) or (2.96, 3.24)
(a) Is the statement correct?
(b) does the interval (2.96, 3.24) cover the true mean? Explain.

3. From a random sample of 70 high school seniors in a large school district, the mean and standard deviation of the verbal scores in the SAT are found to be 424 and 45, respectively. Based on this sample, construct a 98% confidence interval for the mean verbal score in the SAT for the population of all seniors in this school district.

4. Stated here are some claims or research hypotheses that are to be substantiated by sample data. In each case, identify the null hypothesis HÂº and the alternative hypothesis; in terms of the population mean u;.

(a) The mean time a health insurance company takes to pay claims is less that 14 working days.
(b) The average person watching a movie at a local multiplex theater spends over \$2.50 on refreshments.
(c) The mean hospital bill for a birth in the city is less than \$3000
(d) The mean time between purchases of a brand of mouthwash by loyal customers is different from 60 days.

#### Solution Summary

This solution provides step-by-step calculations and explanations for various equations involving statistics.

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