MCQ4 Flashcards
(15 cards)
A team of psychologists studied the effect of multitasking on the completion of cognitive tasks. A group of 40 women participated in the study. Each woman owned a smartphone equipped with the same type of keyboard. The women typed a text passage on the phone twice, one time while sitting in a quiet room (a single task) and the other time while walking (a multitask). The order of the single task and the multitask was randomly determined for each woman. The psychologists recorded the time it took each woman to type the text for both tasks. If the conditions of inference are met, which of the following tests is most appropriate to analyze the data?
A matched-pairs t-test for a mean difference
A produce supplier ships boxes of produce to individual customers. The distribution of weights of shipped boxes is approximately normal with mean 36 pounds and standard deviation 4 pounds. Which expression represents the weight, in pounds, at the 75th percentile of the distribution?
0.67(4) + 36
A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation of the 95 percent confidence level?
We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.
As part of a national sleep study, a random sample of adults was selected and surveyed about their physical activity and the number of hours they sleep each night. Of the 183 adults who exercised regularly (exercisers), 59 percent reported sleeping at least seven hours at night. Of the 88 adults who did not exercise regularly (nonexercisers), 52 percent reported sleeping at least seven hours at night. Which of the following is the most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers?
(0.59)(0.41)/183 + (0.52)(0.48)/88
A representative of a car manufacturer in the United States made the following claim in a news report.
Ten years ago, only 53 percent of Americans owned American-made cars, but that figure is significantly higher today.
A research group conducted a study to investigate whether the claim was true. The group found that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars. A test of the appropriate hypotheses resulted in a p-value of 0.283. Assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago?
No, because 0.283 > 0.05.
Researchers wanted to investigate whether babies have a sense of right and wrong. They showed each of 60 babies a puppet show in which a red puppet was trying to open a heavy box lid. A second puppet, called the helper, would try to help the red puppet open the box, while a third puppet, called the hinderer, would try to slam the box lid down. After watching the show, each baby was presented with a tray containing the helper puppet and the hinderer puppet, and the researchers recorded which puppet the baby reached for. The researchers wanted to determine whether the babies would reach for the helper puppet more than for the hinderer puppet.
As part of the show, a green puppet and a yellow puppet served as the helper and hinderer. For each baby, a coin was tossed to determine which color would serve which role. Which of the following is the most important reason for the random assignment of color to role in the study?
If the same role is played by the same color puppet, the babies might show a preference for the color instead of a preference for the role.
Nutritionists examined the sodium content of different brands of potato chips. Each brand was classified as either healthy or regular based on how the chips were marketed to the public. The sodium contents, in milligrams (mg) per serving, of the chips are summarized in the boxplots below.
The figure shows a boxplot with boxes for Regular Chips and Healthy Chips, with Regular Chips above Healthy Chips. The horizontal axis is labeled Sodium Content in m g and has evenly spaced tick marks numbered from 75 to 300, in increments of 25. The box for Regular Chips starts at about 145 and ends at about 210, with a vertical bar at 175. The whisker on the left side extends from about 105 to the box, and the whisker on the right side extends from the box to about 300. The box for Healthy Chips starts at about 120 and ends at about 220, with a vertical bar at 200. The whisker on the left side extends from about 75 to the box, and the whisker on the right side extends from the box to about 290.
Based on the boxplots, which statement gives a correct comparison between the two classifications of the sodium content of the chips?
The interquartile range (IQR) of the brands classified as healthy is greater than the IQR of the brands classified as regular.
A botanist collected one leaf at random from each of 10 randomly selected mature maple trees of the same species. The mean and the standard deviation of the surface areas for the 10 leaves in the sample were computed.Assume the distribution of surface areas of maple leaves is normal. What is the appropriate method for constructing a one-sample confidence interval to estimate the population mean surface area of the species of maple leaves, and why is the method appropriate?
The t-interval is appropriate, because the population standard deviation is not known.
A state educational agency was concerned that the salaries of public school teachers in one region of the state,region A, were higher than the salaries in another region of the state, region B. The agency took two independent random samples of salaries of public school teachers, one from region A and one from region B. The data are summarized in the table below.
A table is shown with two columns labeled region A and region B. The first row is for mean salary and reads 62583 dollars and 60117 dollars. The second row is standard deviation and reads 6274 dollars and 9319 dollars. The third row is number of salaries and reads 117 dollars and 78 dollars.
Assuming all conditions for inference are met, do the data provide convincing statistical evidence that the salaries of public school teachers in region A are, on average, greater than the salaries of public school teachers in region B?
Yes, there is evidence at the significance level of α = 0.05 but not at α = 0.01.
A florist wanted to investigate whether a new powder added to the water of cut flowers helps to keep the flowers fresh longer than just water alone. For a shipment of roses that was delivered to the store, the florist flipped a coin before placing each rose in its own individual container with water. If the coin landed heads up, the rose was placed in water with the new powder; otherwise, the rose was placed in water alone. Which of the following is the best description of the method used by the florist?
An experiment with a completely randomized design
A commercial for a breakfast cereal is shown during a certain television program. The manufacturer of the cereal wants to estimate the percent of television viewers who watch the program. The manufacturer wants the estimate to have a margin of error of at most 0.02 at a level of 95 percent confidence. Of the following, which is the smallest sample size that will satisfy the manufacturer’s requirements?
2,500
A contestant’s final winnings on a game show are determined by a random selection of a base amount and a possible multiplier. For the base amount, the contestant randomly selects one of four cards, where two cards are marked $1,000, one card is marked $2,000, and one card is marked $5,000. After choosing the card, the contestant randomly selects one of five chips, where three chips are red and two chips are white. If the selected chip is red, the contestant’s final winnings are twice the value of the base amount. If the selected chip is white, the contestant’s final winnings are the value of the base amount. What is the probability that a contestant’s final winnings are exactly $2,000?
0.400
Some contact lens wearers report problems with dryness in their eyes. A study was conducted to evaluate the effectiveness of a new eye-drop solution to relieve dryness for contact lens wearers. Twenty-five volunteers who wore contact lenses agreed to use the new solution for one month. At the end of the month, 36 percent of the volunteers reported that the new solution was effective in relieving dryness. The company that produced the new eye-drop solution concluded that using the new solution is more effective in relieving dryness than using no solution. Which of the following best explains why the study does not support such a conclusion?
The study had no control group.
The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?
0.03+-2.576 (0.03)(0.97)/500
A test of the hypotheses H0 : µ = 0 versus Ha : µ > 0 was conducted using a sample of size 7. The test statistic was t = 1.935. Which of the following is closest to the p-value of the test?
0.0506
