# Confidence interval, sample size

7. Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60 and the standard deviation is 2.30 gallons.

a. What is the point estimate of the population mean?

b. Develop a 99 percent confidence interval for the population mean.

c. Interpret the meaning of part b.

8. Dr. Patton is a Professor of English. Recently he counted the number of misspelled words in a group of student essays. For his class of 40 students, the mean number of misspelled words was 6.05 and the standard deviation 2.44 per essay. Construct a 95 percent confidence interval for the mean number of misspelled words in the population of student essays.

46. Furniture Land South surveyed 600 consumers and found that 414 were enthusiastic about a new home décor they plan to show in their store in High Point, North Carolina. Construct the 99 percent confidence interval for the population proportion.

53. You are to conduct a sample survey to determine the mean family income in a rural area of central Florida. The question is, how many families should be sampled? In a pilot sample of 10 families, the standard deviation of the sample was $500. The sponsor of the survey wants you to use the 95 percent confidence level. The estimate is to be within $100. How many families should be interviewed?

Please show all formulas used and calculations for understanding of material. Please show resources if any for citation.

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#### Solution Preview

7. Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60 and the standard deviation is 2.30 gallons.

a. What is the point estimate of the population mean?

b. Develop a 99 percent confidence interval for the population mean.

c. Interpret the meaning of part b.

a. What is the point estimate of the population mean?

point estimate of population mean= mean obtained from the sample= 8.60 gallons

b. Develop a 99 percent confidence interval for the population mean.

Confidence limits

Mean=M = 8.60 gallons

Standard deviation =s= 2.30 gallons

sample size=n= 60

sx=standard error of mean=s/square root of n= 0.2969 = ( 2.3 /square root of 60)

Confidence level= 99%

Therefore Significance level=alpha (a) = 1% =100% -99%

No of tails= 2

This is a 2 tailed test because we are calculating the confidence interval

Since sample size= 60 >= 30

use normal distribution

Z at ...

#### Solution Summary

Calculates point estimate , confidence interval of mean and proportion, sample size etc.