# Estimates and Confidence interval

1) Which of the following might have resulted from poor sampling design for a survey that attempts to determine the political opinions of the residents of a state?

a. The respondents misrepresent their level of income

b. The sample fails to include a representative portion of minorities

c. In a random sample, 90% indicate that they're Republicans

2) In a simple random sample of 1000 automobile owners between the ages of 25 and 35, there were 142 owners of Ford Explorers. If the expected number of owners of this vehicle was 125 out of 1000, what are the p and n respectively?

3) A marketing consultant is engaged in a project to estimate the proportion of homes receiving both HBO and Showtime cable service. The consultant plans to use a confidence coefficient of 0.95 and a maximum error of the estimate equal to 0.10. If 2500 homes in this city receive cable service, determine the sample size for the consultant to use.

4) The Coca-Cola Company has 40$ of the cola market. Determine the probability that a sample proportion for n=30 is within 0.10 of the true population proportion of 0.40, which represents the proportion of cola drinkers who prefer a Coca-Cola drink.

5) Determine which of the following four population size and sample size combinations would not require the use of the finite population correction factor in calculating the standard error.

a. N=150; n=25

b. N=1500; n=300

c. N=2500; n=75

d. N=15000; n=1000

6) A federal auditor for nationally chartered banks, from a random sample of 100 accounts, found that the average demand deposit balance at the First National Bank of Arkansas was $549.82. If the auditor needed a point estimate for the population mean for all accounts at this bank, what should he use?

a. The average of $54.98 for this sample

b. The average of $539.82 for this sample.

c. There's no acceptable value available

d. The auditor should survey the total of all accounts and determine the mean

7) In order to schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?

8) A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this value is higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows an average of 9.25% with a a standard deviation of 8.61%. Does this sample indicate a smaller average? Use a=0.05 and assume a normally distributed population.

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#### Solution Summary

Solves problems on the topics of sampling design, sample size, population proportion, finite population correction factor, standard error, point estimate of the population mean.

Point Estimate and Confidence Intervals for Standard Deviation

A random sample of n = 9 wheels of cheese yielded the following weights in pounds, assumed to be

N(μ, σ^2):

21.50 18.95 19.40 19.15 22.35 22.90 22.20 23.10

(a) Give a point estimate for σ.

(b) Find a 95% confidence interval for σ and then find a 90% confidence interval for σ.

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