# Statistics chapter review

1) The average cholesterol content of a certain brand of eggs is 224 mg, and the standard deviation is 14 mg. Assume the variable is normally distributed. A sample of 28 eggs is randomly selected.
(a) Describe the sampling distribution of the sample mean (i.e., what distribution, mean, and standard deviation)

(b) Find the probability that the sample mean will be more than 225 mg.

2) A recent study indicated that 27% of the women over age 55 in the study were widows. If 96 women over 55 years of age are randomly selected, what is the probability that at least 22% of them are widows?

3) A sample of 16 randomly selected commuters in Chicago showed the average of the commuting times was 37.2 minutes, and the standard deviation was 7.3 minutes. Assume the population was normally distributed.
(a) Find the 95% confidence interval of the true mean.

(b) Find the 95% confidence interval for the population standard deviation.

4) For the sample data: n = 457, x = 140, find the 90% confidence interval for p hat.

5) An educator wishes to estimate the mean number of hours that 12-year-old children in a city watch television per day. How large a sample is needed if the educator wants to estimate to within 0.5 hour with 98% confidence?
Use = 1.72.

6) A superintendent of a city school system wants to estimate the proportion of parents who believe the school system is providing an adequate education. How large a random sample is needed to estimate the proportion to within two percentage points with 96% confidence?

7) If the confidence interval for is (24.2, 30.4). Find the sample mean (x bar) and the margin of error E.

8)The mean amount of money spent per customer in a department of a retail store is \$38. The department manager claimed he could increase that figure by stocking a new product. The new product was put on the shelves. A sample of 37 customers indicated a mean of \$41 spent with a standard deviation of \$5. Test the managers claim with a 0.01 significance level.

9) According to a local chamber of commerce, in 2013, 5.6% of local area residents owned more than five cars. A local car dealer claims that the percentage has increased. He randomly selects 190 local area residents and finds that 12 of them own more than five cars. Test this car dealers claim at the = 0.05 level of significance.

10) The amount of vitamin C (in milligrams) for 100 gram of various randomly selected fruits and vegetables are listed. Is there sufficient evidence to conclude that the population standard deviation differs from 12 mg? Assume the population is normally distributed. Use = 0.05.
7.9 16.3 12.8 13.0 32.2 28.1 34.4 46.4 53.0 15.4 18.2 25.0 5.2 7.8

11) A local hardware store claims that the mean waiting time in line is less than 3.9 minutes. A random sample of 30 customers has a mean of 3.7 minutes with a standard deviation of 0.8 minute. If = 0.05, test the stores claim using P-value method.

12) A researcher claims that adult hogs fed a special diet will have an average weight of 200 pounds. A random sample of 14 hogs has an average weight of 197.2 pounds and a standard deviation of 3.1 pounds. At = 0.01, can the claim be rejected?

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