Chapter 4: Problem 89
Using the \(\mathrm{p}\) -value given, are the results significant at a \(10 \%\) level? At a \(5 \%\) level? At a \(1 \%\) level? p-value \(=0.2800\)
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Giving a Coke/Pepsi taste test to random people in New York City to determine if there is evidence for the claim that Pepsi is preferred.
Does the airline you choose affect when you'll arrive at your destination? The dataset DecemberFlights contains the difference between actual and scheduled arrival time from 1000 randomly sampled December flights for two of the major North American airlines, Delta Air Lines and United Air Lines. A negative difference indicates a flight arrived early. We are interested in testing whether the average difference between actual and scheduled arrival time is different between the two airlines. (a) Define any relevant parameter(s) and state the null and alternative hypotheses. (b) Find the sample mean of each group, and calculate the difference in sample means. (c) Use StatKey or other technology to create a randomization distribution and find the p-value. (d) At a significance level of \(\alpha=0.01\), what is the conclusion of the test? Interpret the conclusion in context.
Indicate whether it is best assessed by using a confidence interval or a hypothesis test or whether statistical inference is not relevant to answer it. (a) What proportion of people using a public restroom wash their hands after going to the bathroom? (b) On average, how much more do adults who played sports in high school exercise than adults who did not play sports in high school? (c) In \(2010,\) what percent of the US Senate voted to confirm Elena Kagan as a member of the Supreme Court? (d) What is the average daily calorie intake of 20 year-old males?
Exercises 4.29 on page 271 and 4.76 on page 287 describe a historical scenario in which a British woman, Muriel BristolRoach, claimed to be able to tell whether milk had been poured into a cup before or after the tea. An experiment was conducted in which Muriel was presented with 8 cups of tea, and asked to guess whether the milk or tea was poured first. Our null hypothesis \(\left(H_{0}\right)\) is that Muriel has no ability to tell whether the milk was poured first. We would like to create a randomization distribution for \(\hat{p},\) the proportion of cups out of 8 that Muriel guesses correctly under \(H_{0}\). Describe a possible approach to generate randomization samples for each of the following scenarios: (a) Muriel does not know beforehand how many cups have milk poured first. (b) Muriel knows that 4 cups will have milk poured first and 4 will have tea poured first.
Exercise 2.19 on page 58 introduces a study examining whether giving antibiotics in infancy increases the likelihood that the child will be overweight. Prescription records were examined to determine whether or not antibiotics were prescribed during the first year of a child's life, and each child was classified as overweight or not at age 12. (Exercise 2.19 looked at the results for age 9.) The researchers compared the proportion overweight in each group. The study concludes that: "Infants receiving antibiotics in the first year of life were more likely to be overweight later in childhood compared with those who were unexposed \((32.4 \%\) versus \(18.2 \%\) at age 12 \(P=0.002) "\) (a) What is the explanatory variable? What is the response variable? Classify each as categorical or quantitative. (b) Is this an experiment or an observational study? (c) State the null and alternative hypotheses and define the parameters. (d) Give notation and the value of the relevant sample statistic. (e) Use the p-value to give the formal conclusion of the test (Reject \(H_{0}\) or Do not reject \(H_{0}\) ) and to give an indication of the strength of evidence for the result. (f) Can we conclude that whether or not children receive antibiotics in infancy causes the difference in proportion classified as overweight?
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