Name: Open binders and StatCrunch are allowed. For each problem marked with a, follow these directions:

Transcription

1 Units 5 and 6 Units 5 and 6 Group Quiz Name: Holtmann Open binders and StatCrunch are allowed. For each problem marked with a, follow these directions: Sketch a normal curve. Label the mean with a number. Shade in the appropriate area, and label the border(s) of the area with (a) number(s). See the example to the right. Use either StatCrunch or the Empirical Rule. If you use StatCrunch, write StatCrunch and write down the numbers that you type in. If you use the Empirical Rule, write Empirical Rule and label the percentages on your sketch. 1) The Muni busses in San Francisco do not stick to their schedules. Instead, the number of busses that will stop at a certain bus stop between 5:00 and 5:20 p.m. has the probability distribution in the table. Number of Busses Probability ? a) What is the probability that no busses stop at the bus stop between 5:00 and 5:20 p.m.? b) What is the probability that at least one bus stops at the bus stop between 5:00 and 5:20 p.m.? c) What is the probability that exactly one or two busses stop at the bus stop between 5:00 and 5:20 p.m.? d) What is the probability that exactly three busses stop at the bus stop between 5:00 and 5:20 p.m.? e) What is the meaning of probability = zero? the event is impossible p. 1 of 7

2 Airline UNIT 5. PROBABILITY AND PROBABILITY DISTRIBUTIONS 2) The table below shows hypothetical data for two airlines and whether or not their flights arrived on time. Is arriving on time independent of airline? Show work to justify your answer. Arrival Status On Time Late Total United Airlines Virgin America Total P(on time United Airlines) = 60/75 = 0.8 P(on time Virgin America) = 36/45 = 0.8 P(on time) = 96/120 = 0.8 Yes, arriving on time is independent of airline. 3) Public spaces are often designed to accommodate 95% of the population. a) Men have normally distributed heights with a mean of 70 in. (5 10 ) and a standard deviation of 4 in. How tall should a doorway be in order to accommodate 95% of men? 76.6 inches b) Women have normally distributed heights with a mean of 65 in. (5 5 ) and a standard deviation of 3.5 in. The doorway with the height you found in Part (a) will accommodate what percentage of women? P(x 76.6) = or P(x ) = p. 2 of 7

3 4) Assume that the waist girths of men are normally distributed with a mean of 36.7 inches and a standard deviation of 3.5 inches. a) Give a typical interval ( from to ) of belt lengths that would fit a man. from 33.2 to 40.2 inches Empirical rule: mean ± std dev b) What men s waist girths are unusually small? less than 29.7 inches Empirical rule: mean 2 std dev c) Is a man s waist girth of 43 inches unusual? No. Empirical rule: mean 2 std dev d) What is the probability that a randomly selected man has a waist girth of at least 43 inches? e) What is the probability that a randomly selected man has a waist girth less than 43 inches? p. 3 of 7

4 5) A group of researches wanted to know if increased ice cream sales increases shark attacks. To study this, they collected historical data on ice cream sales and shark attacks in California for each month from January 1950 to December a) What is the population? Months from January 1950 to December 2010 b) What is the explanatory variable? Is it categorical or quantitative? Ice cream sales. Quantitative. c) What is the response variable? Is it categorical or quantitative? Number of shark attacks. Quantitative. d) Is the research question about an association or cause-and-effect? How do you know? Cause-and-effect. The word increased indicates that ice cream sales is a cause. e) Are the researchers conducting an observational study of an association between two variables, or an experiment to establish cause and effect? Observational study. f) Name a potential confounding variable. Weather. p. 4 of 7

5 g) Design an experiment to study whether increased ice cream sales increases shark attacks. Use random assignment, a placebo, and a control group to control for the effects of confounding variables. Take a group of experimental subjects who want to go to the beach, and divide them into a treatment group and a control group by some random process, such as flipping a coin (heads = treatment group, tails = control group). My hypothesis is that eating (not buying) the ice cream increases shark attacks, so I will serve ice cream to the treatment group. I also hypothesize that the coldness of the ice cream (as opposed to its calorie content, etc.) is how it increases shark attacks, so will serve cookies (a placebo) to the control group to control for the effects of being hungry and eating sugary food. p. 5 of 7

6 6) Merck Pharmaceutical Company manufactures Propecia, a drug (pill) that Merck claims will treat male pattern baldness on the top of the head and back mid-scalp area in men. For 12 months, doctors studied over 1800 men aged 18 to 41 with mild to moderate amounts of ongoing hair loss. All men, whether given Propecia or a placebo pill, were given a medicated shampoo. In general, men who took Propecia maintained or increased the number of visible scalp hairs and noticed improvement in their hair in the first year, with the effect maintained in the second year. Hair counts in men who did not take Propecia continued to decrease. Merck concluded that Propecia is effective in maintaining or increasing the amount of hair on the top of the head and back mid-scalp area. a) What is the population of this study? men aged 18 to 41 with mild to moderate amounts of ongoing hair loss b) Does Merck s conclusion say that they demonstrated an association or that they proved cause-and-effect? Merck s conclusion says that they proved cause-and-effect. c) Is this an observational study or an experiment? Is it appropriate to the type of conclusion they drew? This is an experiment. Yes, an experiment is appropriate for proving cause-and-effect. d) Is Merck s conclusion valid for the entire population? Why or why not? We can t tell, because the statement doesn t tell us if the sample were randomly selected. e) Name a confounding variable. What methods of controlling the effects of confounding variables are described in the paragraph about Merck s study? The placebo effect is a confounding variable. To control for this, some men were given a placebo pill. f) Name at least one way that the study could be improved. Randomly select the sample of men from the population. p. 6 of 7

7 7) Kaiser Permanente (a health care company) wants to conduct a patient satisfaction survey. Kaiser has 10.2 million health plan members and 38 medical centers across eight states and the District of Columbia. Each member has a seven-digit Kaiser ID number. a) Which one of the following sampling plans will yield the most reliable results? Survey all patients who visit or in any of the medical centers during the month of October. Survey all patients who visit or are in the Antioch medical center during the year Use a random number generator to select 500 member ID numbers, and survey those members. Use a random number generator to select 1000 member ID numbers, and survey those members. 8) Which of the following are advantages of large samples? Check all that apply. Large samples reduce bias. Large samples minimize the effects of confounding variables. The mean values of large samples have less variation, which gives you a more precise answer. Large samples are representative of the entire population. 9) Which of the following are advantages of random samples? Check all that apply. Random samples reduce bias. Random samples minimize the effects of confounding variables. The mean values of random samples have less variation, which gives you a more precise answer. Random samples are representative of the entire population. p. 7 of 7