AP Statistics Unit 8

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

The number of hours a light bulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that

• As we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs of this type.

• The average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.

• The average burnout time of a large number of bulbs has a sampling distribution with similar shape but not as extreme (skewed but not as strongly) as the population distribution.

• The average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

• The average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal.

Which of the following statements about the sampling distribution of the sample mean is incorrect?

• The standard deviation of the sampling distribution will decrease as the sample size increases

• The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.

• The sample mean is an unbiased estimator of the population mean.

• The sampling distribution shows how the sample mean will vary in repeated samples.

• The sampling distribution shows how the sample was distributed around the sample mean.

Why is it important to check the 10% condition before calculating probabilities involving x̄?

• To reduce the variability of the sampling distribution of x̄

• To ensure that the distribution of x̄ is approximately Normal

• To ensure that we can generalize the results to a larger population

• To ensure that x̄ will be an unbiased estimator of μ.

• To ensure that the observations in the sample are close to independent.

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 98% confidence interval for a population mean is found to be 127 ± 18. Which of the following is the correct interpretation of this confidence level?

• The probability that the true mean is contained in this interval is 0.98

• The probability that the sample mean is contained in this interval is 0.98

• The probability that another interval will give a true mean of 127 is 0.98

• If many different random samples of the same size are selected, about 98% of the confidence intervals constructed using this method will contain the value of the population mean

• If many different random samples of the same size are selected, about 98% of the confidence intervals constructed using this method will contain the sample mean of 127

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

I. Increasing the sample size

II. Increasing the confidence level

III. Decreasing the confidence level

• I only

• II only

• III only

• I and II only

• I and III only

You have measured the systolic blood pressure of an SRS of 25 company employees. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which of the following is true?

• 95% of the sample of employees have a systolic blood pressure between 122 and 138

• 95% of the population of employees have a systolic blood pressure between 122 and 138

• If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

• If the procedure were repeated many times, 95% of the time the population mean systolic blood pressure would be between 122 and 128.

• If the procedure were repeated many times, 95 % of the time the sample mean systolic blood pressure would be between 122 and 138.

A salesman who has been in the same job for 10 years is unhappy with his average sales per day of $1,000. He takes a motivation course and randomly chooses eight days’ sales from the month following the course. He computes a 95% confidence interval, obtaining (1019.5, 1265.5). Is there evidence at the 5% level of significance that he has significantly changed his average sales?

• Yes, because the majority of data values are greater than his pre-course mean

• Yes, because the confidence interval does not contain the value 1000

• No, because the post-course mean is not significantly different from 1000

• No, because the confidence interval does not contain the value 1000

• It is impossible to determine whether he has improved, because the confidence interval does not provide a method for making this decision

The Gallup poll said that 39% of a random sample  of 300 people make lunch their big meal of the day.  The standard error of the sample proportion is approximately

• .488
• .032
• .0282