Math IV – Confidence Intervals Quiz 2 (A)

Name: ______Date: ______Period: ____

**Show all work and place final answers in the space provided.**

  • Confidence Interval for proportions Where Z comes from p=CL/2 + 0.5
  • Confidence Interval for means/averagesWhere Z comes from p=CL/2 + 0.5
  1. In 2001, a Gallup poll surveyed 1016 households in the U.S about their pets. Of those surveyed, 599 said they had at least one dog or cat as a pet.
  1. Calculatethe 90% CI for the population proportion.
  1. What is the margin of error for the 90% CI?
  1. Calculatethe 99% CI for the population proportion.
  1. What is the sample size (n=?) if you want to have a 95% Confidence interval with a margin of error of 3% (0.03)?
  1. A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2006. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81kWh.Assuming the standard deviation is unchanged and that the usage is normally distributed,provide an expression for calculating a 99% confidence interval for the mean usage in the March quarter of 2006.

A) C)

B) D)

  1. Strictly speaking, what is the best interpretation of a 95% confidence interval for the mean? Circle.
  1. If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean.
  2. A 95% confidence interval has a 0.95 probability of containing the population mean.
  3. 95% of the population distribution is contained in the confidence interval.
  1. A tire manufacturer wants to examine their tires to make sure that the average tire lasts well on the road. They sampled 50 tires from a batch tire production. Previous research shows that the average tire lasts 40,000 miles on the road with a standard deviation of 1200 miles.
  2. Calculate the 90% CI for the population mean.
  1. What is the margin of error for the 90% CI?
  1. Calculate the 99% CI for the population mean.
  1. What is the sample size (n=?) if you want to have a 95% Confidence interval with a margin of error of 3% (0.03)?

Math IV – Confidence Intervals Quiz 2 (B)

Name: ______Date: ______Period: ____

**Show all work and place final answers in the space provided.**

  • Confidence Interval for proportions Where Z comes from p=CL/2 + 0.5
  • Confidence Interval for means/averagesWhere Z comes from p=CL/2 + 0.5
  1. A tire manufacturer wants to examine their tires to make sure that the average tire lasts well on the road. They sampled 70 tires from a batch tire production. Previous research shows that the average tire lasts 40,000 miles on the road with a standard deviation of 1200 miles.
  1. Calculate the 90% CI for the population mean.
  1. What is the margin of error for the 90% CI?
  1. Calculate the 99% CI for the population mean.
  1. What is the sample size (n=?) if you want to have a 95% Confidence interval with a margin of error of 4% (0.04)?
  1. A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2006. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81kWh.Assuming the standard deviation is unchanged and that the usage is normally distributed,provide an expression for calculating a 99% confidence interval for the mean usage in the March quarter of 2006.

A)C)

B) D)

  1. Strictly speaking, what is the best interpretation of a 90% confidence interval for the mean? Circle.
  1. If repeated samples were taken and the 90% confidence interval was computed for each sample, 95% of the intervals would contain the population mean.
  2. 90% of the population distribution is contained in the confidence interval.
  3. A 90% confidence interval has a 0.90 probability of containing the population mean.
  1. In 2001, a Gallup poll surveyed 2016 households in the U.S about their pets. Of those surveyed, 1099 said they had at least one dog or cat as a pet.
  1. Calculate the 90% CI for the population proportion.
  1. What is the margin of error for the 90% CI?
  1. Calculate the 99% CI for the population proportion.
  1. What is the sample size (n=?) if you want to have a 95% Confidence interval with a margin of error of 4% (0.04)?