ap stats ch 7 ap sets

Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her commute times is approximately normal with mean 20 minutes and standard deviation 2 minutes. When the weather is not good, the distribution of her commute times is approximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probability that the weather will be good tomorrow is 0.9. Which of the following is closest to the probability that Carly's commute time tomorrow will be greater than 25 minutes?

0.0950

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

0.2743

Which of the following statements must be true? The mean of sample H must also be equal to the population mean. The mean of sample G, x¯Gx¯G, is a point estimator for the mean of the population. The mean of sample H, x¯Hx¯H, is a point estimator for the mean of the population.

2 and 3

The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation Which of the following is the best estimate of the standard deviation of the population, sigma x

75

A simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6, respectively. All 10 dice were rolled, and the average of the 10 numbers appearing faceup was recorded. The process was repeated 20 times. Which of the following best describes the distribution being simulated?

A sampling distribution of a sample mean with n = 10, μx̄ = 3.5, and σx̄ ≈ 0.54

A manufacturer of cell phone screens has found that 5 percent of all screens produced have defects. Let pdpd represent the population proportion of all cell phone screens with a screen defect, therefore pd=0.05pd=0.05. For the sampling distribution of the sample proportion of cell phone screens from this manufacturer with a screen defect for sample size 400, μpˆd=0.05μp^d=0.05. Which of the following is the best interpretation of μpˆd=0.05μp^d=0.05 ?

For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.

The distribution of age for players of a certain professional sport is strongly skewed to the right with mean 26.8 years and standard deviation 4.2 years. Consider a random sample of 4 players and a different random sample of 50 players from the population. Which of the following statements is true about the sampling distributions of the sample mean ages for samples of size 4 and samples of size 50 ?

Only the sampling distribution for size 50 will be approximately normal, and the mean for both will be 26.8.

At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B?

Sampling without replacement will result in a standard deviation less than but close to 0.4(0.6)500−−−−−√0.4(0.6)500.

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50.

The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

A certain statistic will be used as an unbiased estimator of a parameter. Let JJ represent the sampling distribution of the estimator for samples of size 40, and let KK represent the sampling distribution of the estimator for samples of size 100. Which of the following must be true about JJ and KK ?

The expected values of JJ and KK will be equal, and the variability of JJ will be greater than the variability of KK.

A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion of those who make a donation when contacted by phone is known to be p=0.05p=0.05. For samples of size 100, which of the following best interprets the mean of the sampling distribution of the sample proportion of people who make a donation when contacted by phone?

The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

The mean and standard deviation of the sample data collected on continuous variable xx are −0.25−0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals Based on the table, do the data support the use of a normal model to approximate population characteristics?

Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.