AP Stats Chapter 8

When interpreting a 95% confidence interval for a population proportion, which of the following is a correct interpretation?

• We can be 95% confident that the sample proportion falls within the interval.

• We can be 95% confident that the interval contains the population proportion.

• There is a 95% chance that any given individual falls within the interval.

• The interval captures the middle 95% of the sample proportions.

What is the point estimate, p̂, of this sample?

• 0.28

• 0.14

• 0.342

• 0.684

The symbol for the sample proportion is __________.

• Z_c

• p̂

• E

• q

Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level?

• We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre

• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.

• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre.

The government claims that 88% of students work during their summer break from college. A random sample of 500 students gave a proportion of 80% and a 95% confidence interval of (.76, .83). Which of the following is a correct interpretation of the 95% level?

• If the study was repeated many times, there is a 95% probability that the true proportion of student that work over the summer is not as the government claims.

• Because 88% is not in our interval, there is a 95% probability that the true proportion of student that work over the summer is not as the government claims.

• If the study was repeated many times, then about 95% of the confidence intervals will contain the true proportion of students that work over the summer college break.

• There is a 95% probability that the true proportion of student that work over the summer is between .76 and 83.

• If the study was repeated many times, then about 95% of the confidence intervals will contain

  .88.

Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Minooka (M), and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Green Bay (G). They intend to perform a confidence interval estimating the true difference of proportion of rainy days between Minooka and Green Bay. Which expression should they use to estimate the standard deviation for the sampling distribution of p̂_M - p̂_G

• a

• b

• c

• d

• e

A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, was found to be (0.236, 0.282).

The point estimate and margin or error for this interval are:

• .236 and .282

• .236 and .046

• unknown and .023

• .259 and .046

• .259 and .023

A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, was found to be (0.236, 0.282).

Which of the following is a correct statement?

• About 95% of the shoppers have between a 23.6% and a 28.2% chance of purchasing cookies.

• There is a 95% probability that the sample proportion lies between 0.236 and 0.282.

• If a second sample was taken, there is a 95% chance that its confidence interval would contain

  0.25.

• This confidence interval indicates that more than 25% of shoppers buy cookies.

• We are reasonably certain the true proportion of shoppers who purchase cookies is between

  24% and 28%.

A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, was found to be (0.236, 0.282). Which of the following would be true about a 98% confidence interval constructed using the same data?

• The interval would be wider, because the standard error would be larger.

• The interval would be narrower, because the standard error would be smaller.

• The interval would be wider, because the critical z* would be larger.

• The interval would be narrower, because the critical z* would smaller.

• The interval would be about the same width, because the standard error would be smaller, but

  the critical z* would be larger.

An SRS of 50 students at a large middle school are asked, “Do you have a television in your bedroom? Twenty-eight of the students responded “yes.” If ƥ = the proportion of students who answered “yes,” what is the standard error of ƥ ?

• .005

• .010

• .070

• .106

• can't be calculated unless we know standard deviation