Homework Assignment #6 (Chapter 12) STAT 1350, Spring 2022 1. A sample of college students enrolled in a General Chemistry course is asked to indicate the number of hours they spent studying for their midterm exam. If you learn the mean of this distribution is 15, what should you conclude? A. Half of the students in the sample spent more than 15 hours studying for their midterm exam. B. The majority of the students in the sample spent less than 15 hours studying for their midterm exam. C. "15 hours" was the most frequent response given when each student was asked how much time they spent studying for the midterm exam. D. The average amount of time spent studying for the midterm exam by this sample of college students was 15 hours. E. All of the above answers are correct interpretations. 2. The are generally less affected by outliers than the A. median and standard deviation; mean and interquartile range B. mean and standard deviation; median and interquartile range C. median and mean; interquartile range and standard deviation D. interquartile range and standard deviation; median and mean E. median and interquartile range; mean and standard deviation3. Although Mcdonald's is a restaurant found all over the world, items on the Mcdonald's menu cost a different amount-in U.S. dollars-depending on what country you are in. Take the Big Mac, for example. In 2021, the cost of the Big Mac, in U.S. dollars, was recorded for a sample of 56 countries. This data is summarized in the boxplot below, and the following statistics were computed: Mean = $3.63, Standard Deviation = $1.21, Minimum = $1.25, Q1 = $2.69, Median = $3.59, Q3 = $4.12, Maximum = $7.29. Based on this information, which one of the following statements is correct? Price (in dollars) A. 75% of the countries in the data set have Big Mac prices that are higher than $4.12. B. The number of countries in the data set that have Big Mac prices between $2.69 and $4.12 is 23. C. 25% of the countries in the data set have Big Mac prices that are between $2.69 and $3.59. D. More than 50% of the countries in the data set have Big Mac prices that are lower than $3.59. E. 75% of the countries in the data set have Big Mac prices that are between $3.59 and $7.29. Which one of the following statements is true? A. It's possible to have a data set in which the standard deviation is larger than the mean. B. A standard deviation will be 0 only if all values in the data set are equal to 0. C. It's impossible for a sample mean to ever be negative. D. An IQR can never be equal to 0. E. A standard deviation will be negative only if all values in the data set are negative.5. Kotzebue is a city located in northern Alaska. In April 2021, the low temperatures in Kotzebue (in degrees Fahrenheit) were recorded for all 30 days of the month. Below is a table of summary statistics that were computed based on these low temperatures. Which of the following statements is a correct interpretation of this information? Mean Standard deviation |Minimum 1 Median Q3 Maximum 7.0 16.71 -21.0 -12.0 14.5 20.5 27.0 A. The IQR is equal to 8.5 degrees Fahrenheit. B. At least 50% of the temperatures in this data set were above 0 degrees Fahrenheit. C. At least one temperature in the data set must have been equal to 14.5 degrees Fahrenheit. D. On average, temperatures in the data set are 32.5 degrees Fahrenheit away from the mean temperature. E. The overall range of temperatures is 6 degrees Fahrenheit. 6. A sample of 15 high school students was asked to indicate the number of hours they spend watching television in a typical week. Their responses are presented in the table below. What is the 50th percentile for this data set? 5 2 10 8 20 5 0 6 19 8 0 14 9 7 A. B. C. 7 D. 8 E. 97. A sample of college students was surveyed and asked about the amount of money they spend each week (in dollars) on "fast food." The data is summarized in the histogram below. Two measures of center were computed for this sample: $23.50 and $27.50. One of these measures is the mean and one is the median. Which measure must be the mean? 10 Frequency OV 60 100 Money spent in a week A. The mean must be $23.50 since the distribution is skewed to the left. B. The mean must be $23.50 since the distribution is skewed to the right. C. The mean must be $27.50 since the distribution is skewed to the left. D. The mean must be $27.50 since the distribution is skewed to the right. E. It's impossible to answer this question without seeing the actual data set. 8. The five-number summary of a set of data is the A. minimum, interquartile range, mean, median, and maximum. B. mean, standard deviation, first quartile, median, and third quartile. C. minimum, mean, median, standard deviation, and maximum. D. mean, median, range, interquartile range, and standard deviation. E. minimum, first quartile, median, third quartile, and maximum.9. The boxplots below were created by an employment agency in order to compare the annual incomes (in thousands of dollars) for a sample of nuclear engineers, a sample of police officers, and a sample of musicians. From an inspection of these boxplots, which one of the following statements must be true? Nuclear engineer Police Profession officer Musician 20 40 60 80 100 120 140 Annual Income (thousands of dollars) A. The median income for the sample of police officers is larger than the median income for the sample of nuclear engineers. B. The median for the sample of nuclear engineers is less than the third quartile (or Q3) for the sample of musicians. C. The incomes of the sample of musicians are less variable than the incomes of the sample of nuclear engineers. D. The largest income comes from a nuclear engineer. E. There are more musicians represented in this data set than police officers. 10. Suppose that you have a data set that includes an even number of data values. You have ordered the values from smallest to largest, and you find the values of 5 and 10 to be right in the middle of the data set. The median would therefore be A. the difference between 5 and 10, which is equal to 5. B. the sum of 5 and 10, which is equal to 15. C. 10 divided by 5, which is equal to 2. D. the average of 5 and 10, which is equal to 7.5. E. the product of 5 and 10, which is equal to 50