Stat 217 – HW 7

Due beginning of class Tuesday, March 9

1) Complete the SATS post-survey. Please remember that your responses are confidential and I will not receive any data until after course grades are submitted.

3) Activity 25-10 (p. 520-1)

· Recall you can use Excel (demo) to make the segmented bar graph or sketch it by hand. Don’t forget to discuss it.

· For the test of significance: define the parameters of interest in words, state Ho and Ha, state and comment on the technical conditions and then use the following output to draw your conclusions.

(g) Also, identify where the largest discrepancy is using the “chi-square contributions.” Discuss what this reveals about the relationship between the treatments and the likelihood of curing Gingivitis.

3) The 1991 World Almanac and Book of Facts contains a section which lists “noted personalities.” These are arranged according to a number of categories, such as “noted writers of the past” and “noted scientists of the past.” One can calculate (approximately, anyway) the lifetimes of these people by subtracting their year of birth from their year of death. It seems natural to wonder whether some occupations tend to have longer lifetimes than others. Distributions of the lifetimes of the people listed in nine different categories have been displayed below, as well as ANOVA computer output.

(a) Which occupation tended to live the longest? Which the shortest?

(b) Why is ANOVA the appropriate analysis for these data? [Hint: Think about what the explanatory and response variables are, and what types of variables they are.]

(d) Below is the corresponding F distribution. Indicate on the graph the value of the test statistic from this study and the p-value.

(e) What conclusion would you draw based on the p-value reported in the output above? In addition to stating your decision about the null hypothesis, be sure to summarize your conclusion about the research question in English, be very clear what population you are willing to generalize to and whether you are drawing a cause and effect conclusion.

(f) Comment on the validity of this analysis as best you can from the information provided. Hint: Which technical conditions do you think are met? How are you deciding? What additional information would you like?

3) Activity 26-9 (p. 543)

Hint: Remember asking for a scatterplot of “y vs x” puts the first one on the y-axis. You can create the scatterplot either in Minitab or by hand.

Add (f) The correlation coefficient in one case is r=-.561 and in the other is r = -.263. Which is the correlation for the full data set and which is the correlation for the data set of just the flights with at least one O-ring failure? Explain.

4) Dansinger, Griffith, Gleason, et al. (2005) report on a randomized, comparative experiment in which 160 subjects were randomly assigned to one of four diet plans: Atkins, Ornish, Weight Watchers, and Zone (40 subjects per diet). These subjects were recruited through newspaper and television advertisements in the greater Boston area; all were overweight or obese with body mass index values between 27 and 52. Among the variables measured were

· Which diet the subject was assigned to

· Whether or not the subject completed the 12-month study

· The subject’s weight loss after 2 months, 6 months, and 12-months (in kilograms, with a negative value indicating weight gain)

· The degree to which the subject adhered to the assigned diet, taken as the average of 12 monthly ratings, each on a 1-10 scale (with 1 indicating complete nonadherence and 10 indicating full adherence).

For the following research questions, indicate which of the following you would perform and state the null and alternative hypotheses (in symbols or in words) in each case. You do not need to carry out the analysis but it would be good for you to briefly justify your choice of procedure! Procedures may be selected more than once or not at all.

i) one sample proportions z-test/interval

ii) one sample means t-test/interval (including matched-pairs)

iii) two-sample proportions z-test/interval

iv) two-sample means t-test/interval

v) chi-square test

vi) anova

vii) regression

1) Does the 12 month weight loss tend to differ from the 2 month weight loss in this population? (Hint: Remember, these are the same subjects!)

2) Is there a statistically significant relationship between the subjects’ adherence levels and 12-month weight loss?

3) Is there convincing evidence that at least half of all dieters on these 4 diets will stay on the diet for at least one year?

4) Did any of the 4 diets lead to significantly different 12-month completion rates (likelihood of staying on the diet for the year)?

5) Are subjects with high adherence levels (at least 7) more likely to complete such a study than subjects with lower adherence levels (less than 7)?