数据分析6.docx

1、数据分析6Question 1Which of the following is not required for the distribution of the sample proportion to be nearly normal?Your AnswerScoreExplanationSample size should be at least 30 and the population distribution should not be extremely skewed.Correct1.00When considering the distribution of the samp

2、le proportion, we dont have a requirement of n 30. To determine if the sample size of categorical data is high enough, we instead check the success-failure condition.Observations should be independent.There should be at least 10 failures.There should be at least 10 successes.Total1.00 / 1.00Question

3、 ExplanationRecognize that the Central Limit Theorem (CLT) is about the distribution of point estimates, and that given certain conditions, this distribution will be nearly normal.In the case of the proportion the CLT tells us that if (1) the observations in the sample are independent, (2) the sampl

4、e size is sufficiently large (checked using the success/failure condition: np10 and n(1p)10), then the distribution of the sample proportion will be nearly normal, centered at the true population proportion and with a standard error of p(1p)n.pN(mean=p,SE=p(1p)n)Question 2When checking conditions fo

5、r calculating a confidence interval for a proportion, you should use which number of successes and failures?Your AnswerScoreExplanationDepends on the contextNot applicable. The number of successes and failures (observed or otherwise) is not part of the conditions required for calculating a confidenc

6、e interval for a proportion.ObservedCorrect1.00Use the observed number of successes and failures when calculating a confidence interval for a proportion, but not when doing a hypothesis test. In a hypothesis test for a proportion, you should usenp0 and n(1 p0) successes and failures; that is, the ex

7、pected number based on the null proportion.Expected (based on the null value)Total1.00 / 1.00Question ExplanationFor confidence intervals use p (observed sample proportion) when calculating the standard error and checking the success/failure condition. For hypothesis tests use p0 (null value) when c

8、alculating the standard error and checking the success/failure condition.Question 3In May 2011, Gallup asked 1,721 students in grades five through twelve if their school teaches them about money and banking. Researchers are interested in finding out if a majority of students receive such education.

9、Which of the following is the correct set of hypotheses?Your AnswerScoreExplanationH0: p = 0.5; HA :p 0.5H0 :p = 0.5; HA:p 0.5Correct1.00The wording of the question tells us were interested in whether the true proportion of students receiving this education is greater than 50% (i.e. makes them “a ma

10、jority”).H0 :p 0.5H0 : = 0.5; HA: 0.5Total1.00 / 1.00Question ExplanationThis question revisits the setup of hypothesis testing within the categorical data / proportions of Unit 5.Question 4You and a friend are about to visit the aviary at the local zoo for the first time. A trustworthy zookeeper sa

11、ys the aviary holds about 3,000 birds. Your friend read somewhere that 10% of those birds are cardinals, but he thinks there are really more cardinals than that. Youre both great at identifying cardinals so you decide to test this claim with a hypothesis test on the true proportion p of cardinals in

12、 the aviary. You walk around the aviary together and get a simple random sample by spotting 250 birds. Of these, 35 were cardinals and 215 were not cardinals. The p-value is 0.0175. Which of the following is false?Your AnswerScoreExplanationp = 0.14H0 :p = 0.10The success-failure condition is met.If

13、 in fact 10% of the birds in the aviary are cardinals, the probability of obtaining a random sample of 250 birds where exactly 14% are cardinals is 0.027.Correct1.00p-value = P(observed or more extreme test statistic | H0true)Total1.00 / 1.00Question Explanationp-value = P(observed or more extreme t

14、est statistic | H0 true)Question 5When do we use the pooled proportion in calculation of the standard error of the difference of two proportions (SE(p1 p2)?Your AnswerScoreExplanationwhen using a randomization test to compare p1 p2when comparing p1 and p2 using a theoretical approach, and the null h

15、ypothesis is H0 : p1 p2 = (some value other than 0)Inorrect0.00Review the associated learning objective.when constructing a confidence interval for p1 p2when comparing p1 and p2 using a theoretical approach, and the null hypothesis is H0 : p1 p2 = 0Total0.00 / 1.00 Question ExplanationNote that the

16、standard error calculation for the confidence interval and the hypothesis test are different when dealing with proportions, since in the hypothesis test we need to assume that the null hypothesis is true. Note that the calculation of the standard error of the distribution of the difference in two in

17、dependent sample proportions is different for a confidence interval and a hypothesis test.Question 6To evaluate the following hypotheses H0 :p = 0.3HA :p 0.3we use a random sample of 50 observations where p = 0.36. Which of the following is the correct standard error? Choose the closest answer.Your

18、AnswerScoreExplanation0.06480.0679Inorrect0.00For a hypothesis test, SE=p0(1p0)n0.00960.02970.00420.0092Total0.00 / 1.00Question ExplanationNote that the reason for the difference in calculations of standard error is the same as in the case of the single proportion: when the null hypothesis claims t

19、hat the two population proportions are equal, we need to take that into consideration when calculating the standard error for the hypothesis test, and use a common proportion for both samples.Question 7An introductory stats professor hypothesizes that 50% of students learn best by watching the video

20、s, 10% by reading the book, 20% by solving questions, and the rest from the discussion forums. She surveys a random sample of a large sample of students asking them how they learn best, and wants to use these data to evaluate her hypothesis. Which method should she use?Your AnswerScoreExplanationZ-t

21、estt-test2 test of goodness of fitCorrect1.00ANOVATotal1.00 / 1.00 Question ExplanationUse a chi-square test of goodness of fit to evaluate if the distribution of levels of a single categorical variable follows a hypothesized distribution. When evaluating the independence of two categorical variable

22、s where at least one has more than two levels, use a chi-square test of independence.Question 8When doing a hypothesis test on a single proportion (i.e. for one categorical variable), we have studied how to calculate the p-value for the hypothesis test, beginning with generating simulated samples. W

23、hich of the following is the best description for how you should generate the simulated samples, and why?Your AnswerScoreExplanationGenerate simulated samples based on the alternative hypothesis because that is the hypothesis were trying to prove when doing the hypothesis test.Generate simulated sam

24、ples based on the null hypothesis because that is the hypothesis were trying to prove when doing the hypothesis test.Generate simulated samples based on the null hypothesis because we need to see how extreme our observed data looks if the null hypothesis were really true.Correct1.00Generate simulate

25、d samples based on the alternative hypothesis because we need to see how extreme our observed data looks if the alternative hypothesis were really true.Total1.00 / 1.00Question ExplanationIn hypothesis testing for one categorical variable, generate simulated samples based on the null hypothesis, and

26、 then calculate the number of samples that are at least as extreme as the observed data.Question 9True or false: In calculation of the required sample size for a given margin of error of the confidence interval for a population proportion, we should use p = 0.5 if we dont have any knowledge about th

27、e characteristics of the population.Your AnswerScoreExplanationTrueCorrect1.00FalseTotal1.00 / 1.00Question 10Suppose in a population 20% of people wear contact lenses. What is the expected shape of the sampling distribution of proportion of contact lens wearers in random samples of 30 people from t

28、his population?Your AnswerScoreExplanationright-skewedCorrect1.00S-F condition not met, and the true population is closer to 0 than 1, so the sampling distribution will be right skewed.uniformleft-skewednearly normalTotal1.00 / 1.00Question ExplanationNote that if the CLT doesnt apply and the sample

29、 proportion is low (close to 0) the sampling distribution will likely be right skewed, if the sample proportion is high (close to 1) the sampling distribution will likely be left skewed.Question 11At a stop sign, some drivers come to a full stop, some come to a rolling stop (not a full stop, but slo

30、w down), and some do not stop at all. We would like to test if there is an association between gender and type of stop (full, rolling, or no stop). We collect data by standing a few feet from a stop sign and taking note of type of stop and the gender of the driver. What are the hypotheses for testing for an association between gender and type of stop?Your AnswerScoreExplanationH0: Gender and type of stop are independent. HA: Gender and type of stop are associated.H0: Males and females are equally likely to come to a rolling stop. HA: Males