In Exercise 2.101 on page 87, we discuss a study about the effect of heat from laptop computers on scrotum temperature in men. Heating the scrotum by just 1^—¦C can reduce sperm count and quality, and repeated increases in temperature can have a longterm effect. In a new study, temperature increases in the right scrotum over one hour were measured in^—¦C while men sat with a laptop computer on their lap. Three different conditions were tested. In Session 1, men sat with legs close together. In Session 2, the legs were kept close together and a lap pad was used to separate the laptop computer from the legs. In Session 3, no lap pad was used but the legs were spread farther apart. The sessions were conducted on three different days with the same volunteers. (Sitting with legs together without a laptop does not increase temperature.) A histogram of the values from Session 2 is shown in Figure A.4, and summary statistics from computer output for all three sessions are shown in Figure A.5.

(a) Describe the shape of the histogram of the temperature changes from Session 2.

(b) How many men participated in each session?

Figure A.4

Figure A.5

(c) Give the summary statistics from Session 1. What are the mean and standard deviation? What is the five number summary?
(d) Find the z-score for the smallest value in Session 3. Is the smallest value more than two standard deviations from the mean?
(e) If the histogram in Figure A.4 makes it appropriate to do so, use the mean and standard deviation from Session 2 to find an interval that is likely to contain 95% of the values. If the shape of the histogram makes this rule inappropriate, say so.
(f) Use the IQR for Session 1 to determine if the largest value in Session 1 is an outlier. Show your work.
(g) Side-by-side boxplots for the three sessions are shown in Figure A.6. Describe what you see. How many outliers are there in each session? Which situation produced the largest temperature increase? Which is more effective at reducing the negative effects of the laptop: using a lap pad or sitting with legs farther apart?

Figure A.6

Exercise 2.101

Studies have shown that heating the scrotum by just 1^—¦C can reduce sperm count and sperm quality, so men concerned about fertility are cautioned to avoid too much time in the hot tub or sauna. A new study suggests that men also keep their laptop computers off their laps. The study measured scrotal temperature in 29 healthy male volunteers as they sat with legs together and a laptop computer on the lap. Temperature increase in the left scrotum over a 60-minute session is given as 2.31 ± 0.96 and a note tells us that €˜€˜Temperatures are given as ^—¦C; values are shown as mean ± SD.€ The abbreviation SD stands for standard deviation. (Men who sit with their legs together without a laptop computer do not show an increase in temperature.)

4 3 TempDIff Frequency 2. Q1 Median 2.328 2.806 1.936 2.475 1.439 Variable Session N Mean StDev Minimum Q3 Maximum 4.915 -0.076 1.571 0.158 1.398 0.534 TempDiff 1 29 2.325 1.058 3.806 3.141 29 1.911 0.747 3 29 1.494 0.617 1.005 1.898