1.Heights, in inches, for the 200 graduating seniors from Washington High School are summarized in thefrequency table below.
Which of the following statements about the median height is true?
(A) It is greater than or equal to 78 inches.
(B) It is greater than or equal to 72 inches but less than 78 inches.
(C) It is greater than or equal to 66 inches but less than 72 inches.
(D) It is greater than or equal to 60 inches but less than 66 inches.
(E) It is less than 60 inches.
2. Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest score was 32 and the lowest was 15. Based on the information displayed in the boxplots above, which of the following statements is true?
(A) Section 1 has the smallest interquartile range.
(B) The lowest score in section 2 is higher than the highest score in either of the other sections.
(C) Section 2 has the smallest range of scores.
(D) The top 25% of scores in section 2 are lower than the highest score in section 3.
(E) At least 50% of the scores in section 3 are higher than all of the scores in section 1.
3. A well-designed experiment should have which of the following characteristics?
I. Subjects assigned randomly to treatments
II. A control group or at least two treatment groups
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
4. The distribution of colors of candies in a bag is as follows.
If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?
1.The graph below shows the monthly average temperatures, in degrees Fahrenheit, for two cities–Madison,Wisconsin, and Juneau, Alaska–in the United States.
(a) Based on the graph, compare the two cities with respect to the monthly average temperatures over the year. Address both similarities and differences in the overall patterns.
(b) For which of the two cities is the standard deviation of the 12 monthly average temperatures greater? Justify your answer without performing any calculations.
2. Researchers investigated the possible beneficial effect on heart health of drinking black tea and whether adding milk to the tea reduces any possible benefit. Twenty-four volunteers were randomly assigned to one of three groups. Every day for a month, participants in group 1 drank two cups of hot black tea without milk, participants in group 2 drank two cups of hot black tea with milk, and participants in group 3 drank two cups of hot water but no tea. At the end of the month, the researchers measured the change in each of the participants’ heart health.
(a) Did the researchers conduct an experiment or an observational study? Explain.
(b) Why did the researchers include a group who drank hot water but no tea?
(c) Is it reasonable to generalize the results of the study beyond the 24 participants? Explain why or why not.
3. Patients experiencing symptoms of a heart attack are routinely transported to a hospital in an ambulance. In a study of a new treatment thought to reduce damage to the heart, patients experiencing symptoms of a heart attack were randomly assigned to one of two groups. During transportation to the hospital, patients in one group received standard care, and patients in the other group received the new treatment consisting of standard care and the application of a blood pressure cuff.
The response variable measured for each patient was a number between 0 and 1, referred to as the myocardial salvage index (MSI). A higher MSI value indicates a more positive outcome for the patient. Summary statistics for the MSI responses of the two groups are shown in the table below.
Do the data provide convincing statistical evidence that the new treatment results in a higher mean MSI value than does the standard care among people similar to the patients in the study?