AP Stats Confidence Intervals for Means

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

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

Mrs. Soto polled 1000 adults and estimated with 90% confidence that the proportion of adults who have dessert after dinner is .75. Ms. Libner thinks that 90% confidence isn't enough and wants to do a 95% confidence. How would a margin of error for 95% compare with a ME for 90% if the same sample size was used?

• It would be smaller because a higher confidence means a smaller MOE

• It would be larger because a higher confidence means a larger MOE

• It would be the same because the sample size is the same

• Won't be able to tell without knowing the true parameter

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

• 1.799

• 1.798

• 1.803

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college. What is the point estimate?

• 75

• 105.2

• 10

• 0.90

A __________ gives an interval of plausible values for the _____________. 

• confidence interval, statistic

• point estimate, parameter

• point estimate, statistic

• confidence interval, parameter

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the Standard Error.

• 75

• 10

• 105.2

• 1.155

Which confidence would result in a wider interval (assuming nothing else changed), 91% or 97%?

• 97%, z* is larger for higher confidence intervals

• 97%, the standard error is larger for higher confidence intervals

• 91%, z* is larger for lower confidence intervals

• 91%, the standard error is smaller for lower confidence intervals

Which of the following is an example of an interval estimate?

• point estimate 

• critical value

• confidence interval

• statistic