AP Stats Review 2017 MC#21-40

Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of all carry-on bags for the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300?

• The bias will decrease and the variance will remain the same.

• The bias will increase and the variance will remain the same.

• The bias will remain the same and the variance will decrease.

• The bias will remain the same and the variance will increase.

• The bias will decrease and the variance will decrease.

Researchers investigated whether a new process for producing yarn could reduce the mean amount of volatile organic compounds (VOCs) emitted by carpet. From random samples of carpets, the researchers found the mean reduction of VOCs emitted by carpets made with yarn produced by the new process compared with that of carpets made with yarn produced by the traditional process was 13 parts per million (ppm). All conditions for inference were met, and the p-value for the appropriate hypothesis test was 0.095. Which of the following statements is the best interpretation of the p-value?

• The probability that the null hypothesis is true is 0.095.

• The probability that the alternative hypothesis is true is 0.095.

• The probability of observing a mean reduction of 13 ppm is 0.095.

• If the null hypothesis is true, the probability of observing a mean reduction of at least 13 ppm is 0.095.

• If the null hypothesis is true, the probability of observing a mean reduction of at most 13 ppm is 0.095.

A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples?

• The margin of error for S will be 4 times the margin of error for R.

• The margin of error for S will be 2 times the margin of error for R.

• The margin of error for S will be equal to the margin of error for R.

• The margin of error for R will be 4 times the margin of error for S.

• The margin of error for R will be 2 times the margin of error for S.

A study was conducted to evaluate the impact of taking a nutritional supplement on a person’s reaction time. One hundred volunteers were placed into one of three groups according to their athletic ability: low, moderate, or high. Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six weeks. At the end of the six weeks, participants were given a coordination task. The reaction time in completing the task was recorded for each participant. The study compared the reaction times between those taking the supplement and those taking the placebo within each athletic ability level.

• A randomized block design

• A completely randomized design

• A matched-pairs design

• A randomized observational study

• A stratified observational study

The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance?

• $2.45

• $2.75

• $24.50

• $29.40

• $36.00

A survey of a random sample of 210 male teens and 228 female teens, ages 13 years to 17 years, found that 122 of the male teens and 160 of the female teens brush their teeth at least twice a day. If there is no difference between the proportions in the population of all male and female teens ages 13 years to 17 years who brush their teeth at least twice a day, approximately how many males and females in the sample would be expected to brush their teeth at least twice a day?

• 105 males and 114 females

• 122 males and 160 females

• 135 males and 147 females

• 141 males and 141 females

• 219 males and 219 females

Researchers believed that an increase in lean body mass is associated with an increase in maximal oxygen uptake. A scatterplot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables. A significance test for the null hypothesis that the slope of the regression line is 0 versus the alternative that the slope is greater than 0 yielded a p-value of 0.04. Which statement is an appropriate conclusion for the test?

• The p-value of 0.04 indicates that 4% of the variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass.

• The p-value of 0.04 indicates that 16% of the variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass.

• The strong positive linear relationship displayed in the scatterplot along with a p-value less than 0.05 indicates that college athletes with higher lean body mass tend to have higher maximal oxygen uptake.

• The strong positive linear relationship displayed in the scatterplot along with a p-value less than 0.05 indicates that an increase in lean body mass causes an increase in maximal oxygen uptake for college athletes.

• A p-value less than 0.05 indicates that the relationship displayed in the scatterplot is likely due to chance, and that there is no statistical evidence of a relationship between lean body mass and maximal oxygen uptake for college athletes.

An environmental group wanted to estimate the proportion of fresh produce sales identified as organic in a local grocery store. In the winter, the group obtained a random sample of sales from the store and used the data to construct the 95 percent z-interval for a proportion (0.087, 0.133). Six months later in the summer, the group obtained a second random sample of sales from the store. The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 percent z-interval for a proportion constructed from the summer sample compare to the winter interval?

• The summer interval is wider and has a lesser point estimate.

• The summer interval is wider and has a greater point estimate.

• The summer interval is narrower and has a lesser point estimate.

• The summer interval is narrower and has a greater point estimate.

• The summer interval is the same width and has a greater point estimate.

In a standard golf tournament, golfers play 18 holes of golf on each of 4 consecutive days. For each hole, golfers keep track of the number of times they hit the ball (strokes) before the ball goes into the cup. A golfer’s score for the tournament is the total number of strokes needed to complete the tournament. The boxplots below summarize the scores for golfers who competed in tournament 1 and golfers who competed in tournament 2. Based on the boxplots, which of the following statements must be true?

• More golfers played in tournament 1 than in tournament 2.

• In both tournaments, at least half the golfers completed the tournament with a score less than 288.

• The number of golfers who completed tournament 1 with a score less than 288 was greater than the number of golfers who completed tournament 2 with a score less than 288.

• The range of scores for tournament 1 is less than the range of scores for tournament 2.

• The score of the golfer with the least score in tournament 1 was greater than the score of the golfer with the least score in tournament 2.

Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewed to the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customer receipts was selected, and the sample mean number of gallons was recorded. Suppose the process of selecting a random sample of 64 receipts and recording the sample mean number of gallons was repeated for a total of 100 samples. Which of the following is the best description of a dotplot created from the 100 sample means?

• The dotplot is skewed to the right with mean 10 gallons and standard deviation 4 gallons.

• The dotplot is skewed to the right with mean 10 gallons and standard deviation 0.5 gallon.

• The dotplot is skewed to the right with mean 10 gallons and standard deviation 0.4 gallon.

• The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon.

• The dotplot is approximately normal with mean 10 gallons and standard deviation 0.4 gallon.