W Q 1. (07.02 HC) Thirty middle-aged women with serum triiodothyronine (T3) readings between 180 nanograms and 200 nanograms per deciliter of blood were selected randomly from a population of similar female patients at a large local hospital. Fifteen of the 30 women were assigned randomly to group A and received a placebo. The other 15 women were assigned to group B and received a new T3 drug. After three months, posttreatment T3 readings were taken for all 30 women and were compared with pretreatment readings. The reduction in T3 level (Pretreatment reading - Posttreatment reading) for each woman in the study is shown here. Group A (placebo) reduction (in nanograms per deciliter): 2, 19, 8, 4, 12, 8, 17, 7, 24, 1, 3, 7, 11, 15, 9 Group B (T3 drug) reduction (in nanograms per deciliter): 30, 19, 18, 17, 20, -4, 23, 10, 9, 22, 17, 21, 13, 31, 15 Part A: Do the data provide convincing evidence, at the a = 0.01 level, that the T3 drug is effective in producing a reduction in mean T3 level? (6 points) Part B: Create and interpret a 99% confidence interval for the difference in the placebo and the new drug. (4 points) B i U Font Family AA A WIN- Y D Q tv[:I Q 2. (07.02 MC) A random sample of 100 chemistry students were asked how many lab classes he or she was enrolled in September 2000. The results showed a mean of 1.65 lab classes with a standard deviation of 1.39. Ten years later, a similar survey was conducted to determine if the distribution changed. The 2010 sample mean was 1.82 with a standard deviation of 1.51. Do the data provide statistical evidence that the mean number of lab classes taken in the rst survey is different from the survey taken 10 years later? Perform the appropriate test using a = 0.02. (10 points) B i g FontFamily vAAv A. ' _=v E v 35 v c358Elmg [:1 D 3. (07.01 LC) The average speed of a volleyball serve is 57 miles per hour. Natalie practiced a new technique to improve her sewing speed. Her coach recorded the speed of 36 random serves during practice and found that her average speed using the new technique was 58.9 miles per hour, with a standard deviation of 2.8 miles per hour. Part A: State the correct hypotheses if Natalie is trying to prove the new technique is an improvement over the old technique. (4 points) Part B: Identify the correct test and check the appropriate conditions. (6 points) B i Q FontFamily vAAv p. '6 __v E v1: v c3fl3llcole A\" cnanges saved [1 [j 4. (07.04 MC) A study was conducted to investigate whether local car mechanics charge women more than men for a transmission repair. The researcher selected randomly one man and one woman from everyone who had used the same mechanic for the same transmission repair. The process was repeated for a total of seven selected randomly cars. The repair prices and the differences are shown in the table. Car1 Car2 Car3 Car4 Car5 Car6 Car7 Women $3,550 $3,200 $1,850 $2,000 $3,000 $1,950 $2,250 Men $3,285 $3,100 $1,975 $2,150 $2,850 $1,750 $2,175 Difference $265 $100 $125 $150 $150 $200 $75 Mean Standard Deviation Women $2,542.86 $691.27 Men $2,469.29 $599.77 Difference $73.57 $157.37 Dotplots of the data and the differences are shown. Women 1,700 1,900 2,100 2,300 2,500 2,700 2,900 3,100 3,300 3,500 3,700 Men 1,700 1,900 2,100 2,300 2,500 2,700 2,900 3,100 3,300 3,500 Difference -200 -150 -100 -50 0 50 100 150 200 250 300 Do the data provide convincing statistical evidence that women pay more than men for the same transmission repair? (10 points) B i U Font Family - AA A F WIN - E #V[:l D 5.(07.05MC) Bailey thinks her heartrate will increase as she increases her biking speed. To see if this relationship exists, she records seven different speeds and models it with a scatterplot and regression output. 130 120 , 110 8 Pulse, beats per minute #0 8 8 'I-l O 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 Speed, miles per hour Regression Statistics Multiple R 97.50557% R Square 95.07336% Adjusted R Square 94.08803% Standard Error 3.884894879 Observations 7 df SS MS F Regression 1 1,456.252245 1,456.252245 96.48906 Residual 75.46204112 15.09240822 Total 6 1531.714286 Coefficients Standard Error t Stat p-Value Intercept 13.55330396 8.879163768 1.526416712 0.187432 Speed 8.651248164 0.880723811 9.822884377 0.000186 Part A: Write the equation of the regression line using the regression output. (2 points) Part B: What do the slope and intercept parameters mean using the context of the problem? (4 points) Part C: Compute the margin of error that Bailey should use if she wants to provide a 96% confidence interval for the slope. Assume that conditions for inference are satisfied. (4 points)