Download Quiz Questions on Statistical Hypothesis Testing and more Quizzes Statistics in PDF only on Docsity! STAT 2 quiz 7: 25 minutes Question 1: To test a roulette wheel is fair, I spin it 500 times. State the appropriate null hypothesis, alternative hypothesis, and test statistic. Question 2: A researcher wishes to study the relationship between mother' heights and daughters' heights. With some effort, she takes a simple random sample of size 200: 100 mother/adult daughter pairs. She finds that daughters are on average 1 inch taller than their mothers, though neither mothers' nor daughters' heights are normally distributed. She performs a two-sample z-test, getting a two-tailed P-value of 16%. She concludes she doesn't have enough evidence to show a statistically significant difference between mothers' and daughters' heights. What has the researcher done wrong? Question 3: I gather data about ethnicity and political views, from a large simple random sample. I divide ethnicity into White, Black, Latino, Asian, and Other. I divide political views into Liberal, Moderate, and Conservative. I wish to test for independence of ethnicity and political views under my categorizations. I decide to do a chi-square test and check its assumptions are satisfied. Under the null hypothesis of independence, how many degrees of freedom will the chi-square distribution for the chi- square statistic have? Question 4: I am performing a two-tailed z-test. My observed average is 2, my expected average under the null is 1, the SD+ of my sample is 10, and my sample size is 100. What is the P-value? Question 5: I am performing a one-tailed t-test. The null hypothesis is that the population mean is zero, while the alternative hypothesis is that the population mean is greater than zero. From a normally distributed sample of size 12, I calculate a t-statistic of 2. I look in a table of t-distributions: Degrees of freedom P(T > 2) 10 3.7% 11 3.5% 12 3.4% 13 3.3% 15 where T is a t-distributed random variable with the stated number of degrees of freedom. What is the P- value? Question 6: A researcher tests a new flu vaccine on a large group of volunteers. The volunteers, all of whom are students at UC Berkeley, are randomly assigned to either the treatment group, which receives the vaccine, or the control group, which receives a placebo. Data is gathered on whether participants get the flu that winter. The results show that a lower percentage of the treatment group got the flu compared to the control group, but the researcher wants to know whether the difference is statistically significant. After checking the study has been appropriately randomised, controlled and double-blinded, a statistician performs a two-sample z-test on the difference between the two groups in the percentage who got the flu. She correctly obtains a P-value of 2%. Did the flu vaccine work for the participants of the study? Will it necessarily work for the whole population? Why or why not?
