STAT 218 HW 3

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University of Nebraska, Lincoln *

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218

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Statistics

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Feb 20, 2024

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Assignment 5 (Chapters 4 and 5) Total Points: 68 Due 10/16/2021 A researcher wanted to see if the fine arts were as entertaining as the movies to UNL students. 58 students were picked for the study. 27 females, and 31 males were selected. The males were sent to a ballet recital, and the females were sent to see a movie. After the show, the researcher measured the percentage of people that responded, “yes,” to the question, “was the show fun to watch”? a. Is this an observational study or an experiment? Explain why. (1+1) Experiment, there are assigned groups with conditions b. What are the observational units? (1) unl students c. What is the explanatory variable? Is it categorical or quantitative? (1+1) how entertaining the ballet recital is vs. a movie, catergorical d. What is the response variable? Is it categorical or quantitative? (1+1) the proportion of people from each group who enjoyed the event, quantitative e. Did this study involve random? If yes, what is the advantage? If no, what is the disadvantage? (1+1) No it was not random, you did not get a representative result for each condition f. An analysis shows there is strong evidence that female like ballet recital more. Can we conclude that the sex of the requester is affecting the rate of liking Fine arts? Why or why not? No because we do not know the proportion of males who liked the ballet recital 2. List the explanatory and the response variable in the following examples. Also, for each of them say if they are categorical or quantitative and try to find the potential confounding variables if there is any. (1+1+1+1+2) The taller you are, the less you pay for your haircut. Response: price Categorical/Quantitative: quantitative Explanatory Variable: height Categorical/Quantitative: categorical Potential Confounding variable: shoe height, faulty chart, liars

It has been observed in a study that the countries with more ice-cream sold reported more drowning deaths in the year 2006. Response: ice cream sales Categorical/Quantitative: quantitative Explanatory Variable: drowning deaths Categorical/Quantitative: quantitative Potential Confounding variable: tourism, weather patterns Many studies have shown that women who smoke while pregnant tend to have babies who weigh significantly less at birth, on average, than women who do not smoke while pregnant. Response: weight of baby Categorical/Quantitative: quantitative Explanatory Variable: women who smoke during pregnancy Categorical/Quantitative: quantitative Potential Confounding variable: genetics, premature birth Based on a survey of almost 3,000 adults, researchers Wyatt et al. (Obesity Research, 2002) reported that those who ate breakfast regularly tended to be more successful at maintaining their weight loss. Response: breakfast or not Categorical/Quantitative: categorical Explanatory Variable: weight loss Categorical/Quantitative: quantitative Potential Confounding variable: exercise, other meals

3. In a 1994 study, 164 pregnant, HIV-positive women were randomly assigned to receive the drug AZT during pregnancy and 160 such women were randomly assigned to a control group that received a placebo. It turned out that 40 of the mothers in the control group gave birth to babies who were HIV-positive, compared to only 13 in the AZT group. Is this an observational study or an experiment? (1) experiment Identify the explanatory and response variables.(State whether they are categorical or quantitative) (1+1+1+1) Explanatory: babies born HIV positive, quantitative Response: drug given, categorical Produce a 2 × 2 table of counts, with the explanatory variable in columns. (4) Born positive 53 Born negative 271 Calculate the proportion of babies who were born HIV-positive in each group. (2+2) AZT group: 13/164 = 7.927% Placebo group: 40/160 = 25% Calculate the relative risk of a baby being born HIV-positive, comparing those in the placebo group to those in the AZT group and interpret it. (2+2) .25/.07927 = 3.15 It is 3.15 times more likely for babies to be born with HIV if their mother was given the placebo than the AZT drug. Produce a standardized statistic. (4) ( .07927 − .25 ) − 0 2 √ .07927 ( 1 − .07927 ) 164 + .25 ( 1 − .25 ) 160 = -4.278

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Take a decision. (2) Fail to reject the null because the z-score is less than 2 Is drug AZT working? (2) Yes it is Set up a 95% Confidence Interval and interpret it. (4+2) .07927 − .25 ± 2 × .0399 = ¿ − .1707 ± .0798 = ¿ (-.2505,.2505) The true proportion of effectiveness of the AZT drug lies between the proportion of (-.2505,.2505) See whether the decision and conclusion from the confidence interval are same as from the standardized statistic. (2+2) Yes they do both come to the same conclusion. The confidence interval says to fail to reject the null hypothesis of H o : p 1 -p 2 =0. The proportions of HIV positive babies from both groups falls within the interval. The standardized statistic suggests to fail to reject the null hypothesis since it is less than the critical value of 2 at -4.278.