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Exam 8: Interval Estimation

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Question 21

Multiple Choice

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We can use the normal distribution to make confidence interval estimates for the population proportion, p, when​

A) ​np > 5.
B) ​n(1 - p) > 5.
C) ​p has a normal distribution.
D) ​both np > 5 and n(1 - p) > 5.

E) None of the above
F) All of the above

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Question 22

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For a given confidence level and when σ is known, the margin of error in a confidence interval estimate

A) ​varies from sample to sample of the same size.
B) ​is the same for all samples of the same size.
C) ​increases as the sample size increases.
D) ​is independent of sample size.

E) None of the above
F) B) and C)

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Question 23

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The makers of a soft drink want to identify the average age of its consumers.A sample of 55 consumers was taken.The average age in the sample was 21 years with a standard deviation of 4 years. a. Construct a 95% confidence interval for the true average age of the consumers. b. Construct an 80% confidence interval for the true average age of the consumers. c. Discuss why the 95% and 80% confidence intervals are different.

A random sample of 100,000 credit sales in a department store showed an average sale of $87.25.From past data, it is known that the standard deviation of the population is $20.00.What is the 95% confidence interval of the population mean?

The mean of the t distribution is​

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 16 pieces of carry-on luggage was weighed.The average weight was 20 pounds.Assume that we know the standard deviation of the population to be 8 pounds.Also, assume the population is normally distributed. a. Determine a 97% confidence interval estimate for the population mean weight of the carry-on luggage. b. Determine a 95% confidence interval estimate for the population mean weight of the carry-on luggage.

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240.The margin of error at 95% confidence is

The dean of a college wants to determine the proportion of students who do not use the campus library.What sample size should he take so that, at 97% confidence, the margin of error will not be more than .1?

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the​

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ) .

Potential sampling error _____as the sample size increases.

The manager of a grocery store has taken a random sample of 144 customers.The average length of time it took these 144 customers to check out was 3 minutes.It is known that the standard deviation of the population of checkout times is 1 minute.The 95% confidence interval for the true average checkout time (in minutes) is

In order to estimate the average electric usage per month, a sample of 64 houses was selected and the electric usage was determined.Assume a population standard deviation of 320 kilowatt-hours.The standard error of the mean is

In interval estimation, as the sample size becomes larger, the interval estimate

A simple random sample of 144 items resulted in a sample mean of 1257.85 and a standard deviation of 480.Develop a 95% confidence interval for the population mean.

You are given the following information obtained from a random sample of 5 observations taken from a large population. ​ Construct a 95% confidence interval for the mean of the population, assuming the population has a normal distribution.

A random sample of 100,000 credit sales in a department store showed an average sale of $87.25.From past data, it is known that the standard deviation of the population is $20.00.With a .95 probability, determine the margin of error.

You are given the following information obtained from a random sample of 6 observations.Assume the population has a normal distribution. ​ a. What is the point estimate of μ? b. Construct an 80% confidence interval for μ. c. Construct a 98% confidence interval for μ. d. Discuss why the 80% and 98% confidence intervals are different.

A random sample of 53 observations was taken.The average in the sample was 90 with a variance of 400. a. Construct a 98% confidence interval for μ. b. Construct a 99% confidence interval for μ. c. Discuss why the 98% and 99% confidence intervals are different. d. What would you expect to happen to the confidence interval in Part a if the sample size was increased? Be sure to explain your answer.

The technical support department at Apple, Inc.sampled 100,000 calls and reported that the mean of time a customer is placed on hold is 4.5 minutes.Assume a standard deviation of 1.75 minutes.Provide a 95% confidence interval estimate for the true average time a customer was placed on hold.