Inference Review: Name That Test
For each problem, name (be specific) the type of test to be carried out and state the hypotheses (in symbols AND words) for that test.
1. Fruit flies show a daily cycle of rest and activity. A study used an infrared motion sensor to see if flies moved in response to vibrations. Here are the results:
Response to vibration?
NoYes
Fly was walking1054
Fly was resting284
Is there good reason to think that resting flies respond differently than flies that are walking? Give appropriate statistical evidence to support your answer.
2. During a given 2 week period, the participants in the study received the same type of potato chip (regular or fat free) each day. After the 1st 2 week period, there was a 1-week washout period in which no testing was performed. There was then another 2-week period in which the participants received the alternate type of potato chip (reg. or fat free) each day under the same protocol. One response variable was the weight in grams of potato chips that a subject ate. We want to compare the amounts of regular and fat-free chips eaten. Is there a significant difference in the amount of regular and fat free chips consumed?
3. A study compared normal mice bred to spontaneously developed diabetes. The investigators attached sensors to the right hip and front feet of the mice and measured the difference in electrical potential (millivolts) between these locations. Here is the data
Diabetic mice14.7010.009.8010.85
13.6022.6011.7010.30
Normal mice13.807.209.508.40
9.1010.0010.408.55
Is there significant evidence of a difference in mean potentials between the two groups?
4. In a 2004 sample of 2158 students, 1014 had at least one college graduate parent. Is there evidence that over half of all students have at least one college graduate parent?
5. The distribution of grades for the hundreds of students taught by TA’s at a college this semester is:
GradeABCD/F
Probability.32.41.2.07
The grades taught by a professor for 91 students were
GradeABCD/F
Count:22382011
Is there good evidence that the professor’s grade distribution differs from the TA’s grade distribution?
6. The study times of all first year university students follow a normal distribution with standard deviation 65 minutes. A student group claims first year students must study at least 2.5 hours a week. A skeptic suspects they study less than that on average. A class survey finds that the average study time claimed by 269 students is x-bar = 137 min. Is this good evidence to support the skeptic’s claim?
7. A study by the National Athletic Trainers Association surveyed 1679 HS freshmen and 1366 HS seniors. Results showed that 34 freshmen and 24 seniors had used anabolic steroids. Is there a significant difference in the rate of anabolic steroid use by the grade levels at this high school?
8. Coffee is a leading export from several developing countries. When coffee prices are high, farmers often clear forest to plant more coffee trees. Here are 5 years’ data on prices paid to coffee growers and the percent of area lost in a national park that lies in a coffee producing region.
Price (cents/lb)2940545571
Forest lost (%).491.591.691.823.1
Computer output gives the following
Forest lost = -1.0134 + .0552 x price, r2 = .91
Do you think that coffee will allow good prediction for forest lost? Explain.
9. Here are the estimates of the daily intakes of calcium (in mg) for 10 women age 18-24 who participated in a study of women’s bone health.
808 6516261156882
7167746841062438
Suppose that the recommended daily allowance (RDA) of calcium for women this age range is 1200 mg. Doctors involved suspect the subjects had significantly lower calcium rates than the RDA. Test the doctor’s claim.