Unit 6 Sampling Distributions for Proportions Review

A machine is used to fill bags with a popular brand of trail mix. The machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. Of the following, which is the least weight of a bag in the top 5 percent of the distribution?

• 234 grams

• 240 grams

• 243 grams

• 246 grams

• 248 grams

Tags

CCSS.HSS.ID.A.4

The height requirement for a certain ride at an amusement park is 48 inches or taller. The distribution of height of six-year-old children is approximately normal with mean 45.2 inches and standard deviation 1.75 inches. Which of the following is closest to the probability that a randomly selected six-year-old child will not meet the height requirement for the ride?

• 0.0401

• 0.0548

• 0.9452

• 0.9599

• 0.9974

Tags

CCSS.HSS.ID.A.4

A certain statistic d̂ is being used to estimate a population parameter D. The expected value of d̂ is not equal to D. What property does d̂ exhibit?

• The sampling distribution of d̂ is normal.

• The sampling distribution of d̂ is binomial.

• The sampling distribution of d̂ is uniform.

• d̂ is unbiased.

• d̂ is biased.

Which of the following conditions will create a biased estimator of a population parameter?

• The sampling distribution of the estimator is skewed to the left.

• The sampling distribution of the estimator is skewed to the right.

• The sampling distribution of the estimator is not the same shape as the distribution of the population parameter.

• The expected value of the estimator is not equal to the population parameter.

• The variability of the sampling distribution of the estimator is not equal to the variability of the population parameter.

The following graphs show the sampling distributions for two different point estimators, R and W, of the same population parameter. Which of the following statements is true?

• Both R and W are unbiased.

• Both R and W are biased.

• R is biased, and W is unbiased.

• R is unbiased, and W is biased.

• The assessment of bias is not possible, because the sampling distributions display too much variability.

According to data from the United States Elections Project, only 36 percent of eligible voters voted in the 2014 elections. For random samples of size 40, which of the following best describes the sampling distribution of p̂, the sample proportion of people who voted in the 2014 elections?

• The sampling distribution is skewed to the left, with mean 0.36 and standard deviation 0.076.

• The sampling distribution is skewed to the right, with mean 0.64 and standard deviation 0.006.

• The sampling distribution is approximately normal, with mean 0.36 and standard deviation 0.076.

• The sampling distribution is approximately normal, with mean 0.36 and standard deviation 0.006.

• The sampling distribution is approximately normal, with mean 0.64 and standard deviation 0.076.

For a certain population of sea turtles, 18 percent are longer than 6.5 feet. A random sample of 90 sea turtles will be selected. What is the standard deviation of the sampling distribution of the sample proportion of sea turtles longer than 6.5 feet for samples of size 90?

• For all samples of size 100, the mean of all possible sample proportions of monitors manufactured that have a screen defect is 0.04.

• For all samples of size 100, the standard deviation of all possible sample proportions of monitors manufactured that have a screen defect is 0.04.

• For a randomly selected screen monitor, the probability that the selected monitor will have a screen defect is 0.04.

• For each sample of size 100, the proportion of monitors manufactured that will have a screen defect is 0.04.

• For a randomly selected screen monitor, the mean number of defects for the monitor will be equal to 4.

According to a recent survey, 47.9 percent of housing units in a large city are rentals. A sample of 210 housing units will be randomly selected. Which of the following must be true for the sampling distribution of the sample proportion of housing units in the large city that are rentals to be approximately normal?

• The distribution of the population must be approximately normal.

• The sample size must be greater than 30.

• The sample size must be less than 10 percent of the size of the population.

At a national convention attended by many educators, about 30 percent of the attendees are from the northeast. Of all the attendees of the national convention, 25 will be selected at random to receive a free book. What are the mean and standard deviation of the sampling distribution of the proportion of attendees from the northeast for samples of size 25?