1. Researchers conducted a telephone survey of 427 adults living in a large city. The adults were asked whether they planned to purchase a smart watch in the next year. The table shows the responses categorized by the region of the city in which the residents live.
Which of the following graphical displays is most appropriate for comparing the proportions of those surveyed who plan to purchase a smart watch within the four regions?
(A) A scatterplot
(B) A boxplot
(C) A segmented bar chart
(D) A back-to-back stemplot
(E) A dotplot
2.A scientist recorded the duration of the eruptions of the Old Faithful geyser in Yellowstone National Park that occurred during a one-month time period. The histogram below shows the distribution of the duration, in seconds, of the eruptions.
Based on the histogram, which of the following is the best description of the distribution?
(A) The distribution is uniform, is centered at about 200 seconds, and has a range of at most 250 seconds.
(B) The distribution is skewed to the left, is centered at about 125 seconds, and has a range of at most 250 seconds.
(C) The distribution is skewed to the right, is centered at about 260 seconds, and has a range of at most 250 seconds.
(D) The distribution displays two clusters, has a range of at most 200 seconds, and includes outliers below 75 seconds and above 325 seconds.
(E) The distribution displays two clusters, with one cluster centered at about 125 seconds and the other centered at about 260 seconds, and has a range of at most 250 seconds.
3. Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?
(A) P(E)= 0.12
(B) P(E)= 0.4
(C) P(D or E) = 0.28
(D) P(D or E) = 0.72
(E) P(D or E)= 0.9
4. Researchers used two footballs of the same size to examine the effect of helium on kicking distance. One football was filled with air, and the other was filled with helium. Eleven people participated in the study. Each person kicked the football filled with air and the football filled with helium, and the kicking distances, in yards,were recorded. The football that was kicked first was determined by the flip of a fair coin, and the people did not know which football was filled with air and which was filled with helium. What type of study was conducted by the researchers and, of the following, which is the appropriate t-interval for inference?
(A) A completely randomized design and a t-interval for a difference between means for independent samples
(B) A completely randomized design and a t-interval for a mean difference
(C) A matched-pairs design and a t-interval for a difference between means for independent samples
(D) A matched-pairs design and a t-interval for a mean difference
(E) An observational study and a t-interval for a difference between means for independent samples
1. Population pyramids are a type of bar chart that show the distribution of ages of a country’s population. The distributions of ages of men and women for two countries, A and B, for the year 2015 are shown in the population pyramids below. The age-groups, in years, are listed in the center columns, and the proportions are shown on the horizontal axes. Each bar represents the proportion of the age-group in the population for that sex.
(a) Is the proportion of the female population age 60 or older in Country A greater than the proportion of the female population age 60 or older in Country B? Justify your answer.
(b) One of the two countries experienced an increase in the birth rate in the years 1946 to 1955 and another increase in the birth rate about 20 years later. Based on the graphs, which country experienced the described increases in birth rate? Justify your answer using information from the graphs.
(c) For Country A, in which age-group is the median age of the male population? Justify your answer.
2. The ability to visually search, such as when reading an x-ray or interpreting a satellite image, is an important skill in many jobs. Researchers conducted a study to investigate whether playing video games could improve a person’s ability to visually search. Three video games were used in the study: one was a driving game, one was a sports game, and one was a puzzle game. The participants consisted of 60 volunteers who had no experience playing video games before the study. Each participant was randomly assigned to one of the three games so that there were 20 participants per game.
(a) Describe an appropriate method for randomly assigning 60 participants to three groups so that each group has 20 participants.
The time to complete a visual search task was recorded for each participant before the assigned game was played. The time to complete a visual search task was again recorded for each participant after the assigned game was played. For each game, the mean improvement time (time before minus time after) was calculated.
(b) One researcher expressed an interest in investigating whether playing a driving game would lead to a different mean improvement time to complete a visual search task than would playing a sports game.Assuming the appropriate population values are approximately normally distributed, state the name of a test with the appropriate null and alternative hypotheses that could be used to investigate the researcher’s interest.
(c) When the appropriate test was performed, no significant difference was found in mean improvement time between the driving game and the sports game. Name one change the researchers could make in a future study to increase the power of the test. Explain why such a change would increase the power.