AP Stats Confidence Intervals for a Mean

You want to calculate a 98% confidence interval for a population mean with a sample of n = 20. What is the appropriate t*?

• 2.326

• 2.528

• 2.539

• 2.518

A researcher wants to find a confidence interval estimate of the mean time it takes to complete an order over the phone at a call center for a large retail company. He has selected a random sample of 18 orders and recorded the time to complete the order. The sample mean time was 4.27 minutes and the sample standard deviation was 0.78 minutes. Assuming the conditions needed for inference are met, which of the following is the appropriate 98% confidence interval?

• 4.27 ± 2.326 ⋅ (0.78/√18)

• 4.27 ± 2.054 ⋅ (0.78/√18)

• 4.27 ± 2.552 ⋅ (0.78/√18)

• 4.27 ± 2.567 ⋅ (0.78/√18)

• 4.27 ± 2.567 ⋅ (0.78/√17)

Which of the following would not decrease the width of a confidence interval?

• I only

• II only

• III only

• I and II only

• II and III only

An irate patient complained that the cost of a doctor's visit was too high.  She randomly surveyed 20 other patients and found that the mean amount of money they spent on each doctor's visit was $44.80.  The standard deviation of the sample was $3.53.  Find the 95% confidence interval of the population mean.

• $43.15 - $46.45

• $44.53 - $48.21

• $42.65 - $48.25

• $43.15 - $48.25

2000 children were surveyed and the report that followed said, "With 98% confidence, between 20% and 50% of all parents make their children eat breakfast." What does 98% confidence mean in this situation?

• We can be 98% confident that the method used to get the intervals always gives the correct answer

• 98% of all parents will make their kids eat breakfast

• When used repeatedly, the method used to find the interval produces intervals which include the true proportion about 98% of the time

• The kids were 98% confident that they ate breakfast that day.

The heights of 5-year old boys are approximately normal. The mean height of a random sample of 37 5-year old boys is found to be 30 inches with a standard deviation of 3 inches. What is the standard error of x̄?

• .493

• 1.32

• 5.77

• 1.96

Mrs. Soto wants to find the sample size needed to find with 95% confidence the mean amount of time her stats students spent on homework during the snow days. The population is approximately normal and the known standard deviation is 6 minutes. How large should the sample size be if she wants a margin of error of +- .5 minutes?

• 553

• 551

• 600

• 601

Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT Math scores. Suppose that you do this many, many times. Which of the following are the mean and standard deviation of the sampling distribution of x̄ ?

• Mean = 515; SD = 114

• Mean = 515; SD = 114/√100

• Mean = 515/100; SD = 114/√100

• Mean = 515/100; SD = 114/100

• Mean = 515/100; SD = 114/√100

One reason for using a t distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

• z can be used only for large samples

• z requires that you know the population standard deviation

• z requires that you can regard your data as an SRS from the population

• z requires that the sample size is at most 10% of the population size

• a z critical value will lead to a wider interval than a t critical value

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.