MCQ 5 Flashcards
(15 cards)
As part of a community service program, students in three middle school grades (grade 6, grade 7, grade 8) each chose to participate in one of three school-sponsored volunteer activities. The graph below shows the distribution for each class for the three activities.
The figure shows a horizontal bar graph with the horizontal axis labeled from zero percent to 100 percent in increments of 20. There are three bars on the graph, labeled on the left from top to bottom: Grade 8, Grade 7, and Grade 6. A key on the graph shows the parts of the bars that represent Activity A, Activity B, and Activity C. The bars are as follows, from top to bottom and left to right: Grade 8, Activity A: zero percent to about 25 percent; Activity B: about 25 percent to about 63 percent; Activity C: about 63 percent to 100 percent. Grade 7, Activity A: zero percent to about 24 percent; Activity B: about 24 percent to 60 percent; Activity C: 60 percent to 100 percent. Grade 6. Activity A: zero percent to 20 percent; Activity B: 20 percent to 80 percent; Activity C: 80 percent to 100 percent.
Based on the graph, which statement must be true?
For students in grade 7, the number who chose activity C was greater than the number who chose activity B.
At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatterplot of the two variables indicated a strong, positive linear association between the variables. Which of the following statements is a correct interpretation of the word “strong” in the description of the association?
The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model.
A group of men and women were surveyed to investigate the association between gender and the number of friends the person has on a social media Web site. Results are shown in the table below.
A table is shown with five columns under the heading number of friends. The columns are labeled 0 to 50, 51 to 100, 101 to 150, 151 to 200, and 201 or more. The first row is for men and reads 17, 82, 73, 56, and 42. The second row is for women and reads 45, 73, 98, 87, and 75.
Which of the following procedures is the most appropriate for investigating whether an association exists between gender and the number of friends a person has on a social media Web site?
A chi-square test of independence
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
The number of siblings was recorded for each student of a group of 80 students. Some summary statistics and a histogram displaying the results are shown below.
A table is shown with two rows. The top row reads mean, standard deviation, Q 1, and Q 3. The second row reads 3.5, 2.535, 2, and 5.
The figure shows a histogram with the horizontal axis labeled Number of Siblings and the left vertical axis labeled Frequency. The numbers from 0 through 12 appear along the horizontal axis from left to right. The numbers zero through 16, in increments of 2, appear along the vertical axis from bottom to top. The numbers along the horizontal axis are centered under each bar. The bar heights are as follows, from left to right: Bar at zero: 7. Bar at 1: 12. Bar at 2: 14. Bar at 3: 12. Bar at 4: 10. Bar at 5: 9. Bar at 6: 7. Bar at 7: 3. Bar at 8: 2. Bar at 9: 2. Bar at 10: 1. Bar at 11: There is no bar. Bar at 12: 1.
An outlier is often defined as a number that is more than 1.5 times the interquartile range below the first quartile or above the third quartile. Using the definition of an outlier and the given information, which of the following can be concluded?
The median is less than the mean, and the distribution has two outliers.
In the states of Florida and Colorado, veterinarians investigating obesity in dogs obtained random samples of pet medical records and recorded the weights of the dogs in the samples. A test was conducted of H0 : p1 = p2 versus Ha : p1 ≠ p2, where p1 represents the proportion of all overweight dogs in Florida and p2 represents the proportion of all overweight dogs in Colorado. The resulting test statistic for a two-sample z-test for a difference between proportions was 1.85. At the significance level α = 0.05, which of the following is a correct conclusion?
There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05.
A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design?
Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.
A controversial issue in the sport of professional soccer is the use of instant replay for making difficult goal line decisions. Each person in a representative sample of 102 players, fans, coaches, and officials was asked his or her opinion about the use of instant replay for goal-line decisions. The data are summarized in the two-way frequency table below.
A table is shown with columns showing opinion and rows showing category. The first column is favor use and the second column is oppose use. The first row is for players and has entries 22 and 2. The second row is for fans and has entries 18 and 6. The third row is for coaches and has values 15 and 26. The fourth row is for officials and has values 3 and 10.
In testing to see whether opinion with respect to the use of instant replay is independent of the category of the person interviewed, a chi-square test statistic of 27.99 and a p-value less than 0.001 were calculated. Which of the following statements is correct?
The small p-value suggests that there is evidence of an association between category and opinion about the use of instant replay.
A marketing research consultant for a hotel chain hypothesizes that men and women differ in their color preference for guest rooms. The consultant shows pictures of rooms decorated with three different color scheme to each person in a random sample of 110 men and to each person in a random sample of 90 women. The consultant asks each person to choose his or her favorite color scheme. A chi-square test for homogeneity of proportions will be used to test the consultant’s hypothesis. Assuming that the conditions for inference are met, which of the following statements is true for the test?
The more that men and women differ in their color preferences, the larger the chi-square statistic will be.
Which of the following statements must be true about the data sets A and B displayed in the histograms above?
The standard deviation of data set A is greater than the standard deviation of data set B.
Makers of a new pain-relieving medication claim that it relieves chronic pain faster than the current top-selling pain reliever on the market. A double-blind experiment was conducted in which 10 people who experience chronic pain were randomly selected to take either the new or the current medication. Each of the 10 people recorded the time, in minutes, from taking the medication until pain relief. After an appropriate time period, each of the 10 people took the other medication and recorded the time from taking the medication until pain relief. The medication each person took first was randomly determined, and because both medications look the same, the people in the study did not know which medication was taken first. The table below shows summary statistics for the results.
A table is shown with three columns. The first two columns, new medication and current medication, and under the larger heading of minutes until pain relief. The third column is labeled difference, new minus current. The first row is mean and reads 15.600, 16.025, and negative 0.425. The second row is standard deviation and reads 4.811, 4.833, and 1.395.
Which of the following values is closest to the p-value of the appropriate t-test?
0.1802
The table below shows historical data for the distribution of the number of customers, in half-hour time periods, who visit the electronics department of a retail store. For example, in 25 percent of the time periods for which data were collected, no customers were observed in the electronics department of the store.
A table is shown with two rows. The first row reads number of customers, 0, 1, 2, and 3 or more. The second row reads proportion of time periods, 0.25, 0.20, 0.30, and 0.25.
To investigate if the distribution has changed, the number of customers who visited the electronics department of the store was recorded for each of 50 randomly selected time periods. The results are shown in the table below.
A table is shown with two rows. The first row reads number of customers, 0, 1, 2, and 3 or more. The second row reads number of time periods, 4, 13, 14, and 19.
A chi-square goodness-of-fit test was conducted to determine whether the data provide convincing evidence that the distribution has changed. The test statistic was 10.13 with a p-value of 0.0175. Which of the following statements is true?
At the significance level α = 0.05, the data provide convincing evidence that the current distribution is different from the historical distribution.
A group of students wanted to investigate the claim that the average number of text messages sent yesterday by students in their school was greater than 100.
Because p > 0.05, at the 5% significance level, it cannot be concluded that the mean number of text messages sent yesterday by students in the school is greater than 100.
Because p > 0.05, at the 5% significance level, it cannot be concluded that the mean number of text messages sent yesterday by students in the school is greater than 100.
A sample of 942 homeowners are classified, in the two-way frequency table below, by the number of credit cards they have and the number of years they have owned their current homes.
A table is shown with five columns labeled number of credit cards, less than one year, one year to three years, more than three years, and total. The last four columns all fall under the heading number of years owning current home. The first row reads 1, 265, 53, 16, and 334. The second row reads 2, 84, 19, 4, and 107. The third row reads 3, 201, 68, 20, and 289. The fourth row reads 4 or more, 134, 58, 20, and 212. The last row reads total, 684, 198, 60, and 942.
Of the homeowners in the sample who have four or more credit cards, what proportion have owned their current homes for at least one year?
78/212
Jessica wanted to determine if the proportion of males for a certain species of laboratory animal is less than 0.5. She was given access to appropriate records that contained information on 12,000 live births for the species. To construct a 95 percent confidence interval, she selected a simple random sample of 100 births from the records and found that 31 births were male.
Based on the study, which of the following expressions is an approximate 95 percent confidence interval estimate for p, the proportion of males in the 12,000 live births?
0.31+-1.96 (0.31)(0.69)/100
