数据分析33.docx

1、数据分析33Question 1We want to estimate the average coffee intake of Coursera students, measured in cups of coffee. A survey of 1,000 students yields an average of 0.55 cups per day, with a standard deviation of 1 cup per day. Which of the following is not necessarily true?Your AnswerScoreExplanation=0.

2、55, =1Correct1.00Just because the sample statistics are these values doesnt mean the population values will be exactly equal to them, therefore its not necessarily true that =0.55, =1.x=0.55, s=1The sample distribution is right skewed.0.55 is a point estimate for the population mean.Total1.00 / 1.00

3、Question ExplanationThis question refers to the following learning objective(s): Define sample statistic as a point estimate for a population parameter, for example, the sample mean is used to estimate the population mean, and note that point estimate and sample statistic are synonymous.Question 2Re

4、searchers studying anthropometry collected various body and skeletal measurements for 507 physically active individuals. The histogram below shows the sample distribution of heights in centimeters. If the 507 individuals are a simple random sample - and lets assume they are - then the sample mean is

5、 a point estimate for the mean height of all active individuals. What measure do we use to quantify the variability of such an estimate? Compute this quantity using the data from this sample and choose the best answer below.Your AnswerScoreExplanationstandard deviation = 0.417standard error = 0.417m

6、ean squared error = 0.105standard deviation = 0.019standard error = 0.019Inorrect0.00We quantify variability in the sample mean by calculating the standard error (of the mean) SE=/n.Total0.00 / 1.00Question ExplanationThis question refers to the following learning objective(s): Calculate the samplin

7、g variability of the mean, the standard error, as SE=/n.Question 3The standard error measures:Your AnswerScoreExplanationthe variability of sample statisticsthe variability of population parametersthe variability in the populationthe variability of the sampled observationsInorrect0.00The variability

8、 of the sampled observations is measured by the sample standard deviation s.Total0.00 / 1.00Question ExplanationThis question refers to the following learning objective(s): Distinguish standard deviation ( or s) and standard error (SE): standard deviation measures the variability in the data, while

9、standard error measures the variability in point estimates from different samples of the same size and from the same population, i.e. measures the sampling variability.Question 4Suppose you took a large number of random samples of size n from a large population and calculated the mean of each sample

10、. Then suppose you plotted the distribution of your sample means in a histogram. Now consider the following possible attributes of your collected data and the population from which they were sampled. For which of the following sets of attributes would you not expect your histogram of your sample mea

11、ns to follow a nearly normal distribution?Your AnswerScoreExplanationn = 120. The population distribution is unknown, but the distribution of data in each sample is slightly skewed.n = 20. The population distribution is nearly normal.n = 120. The population distribution is slightly skewed.n = 10. Th

12、e population distribution is unknown, but the distribution of data in each sample is heavily skewed.Correct1.00Sample size is small and the population distribution might be skewed, hence likely not going to yield nearly normal sampling distribution.Total1.00 / 1.00Question ExplanationThis question r

13、efers to the following learning objective(s): Recognize 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 mean the CLT tells us that if (1a) the sample size is sufficiently

14、large (n30) and the data are not extremely skewed or (1b) the population is known to have a normal distribution, and (2) the observations in the sample are independent, then the distribution of the sample mean will be nearly normal, centered at the true population mean and with a standard error of n

15、.xN(mean=,SE=n)When the population distribution is unknown, condition (1a) can be checked using a histogram or some other visualization of the distribution of the observed data in the sample.The larger the sample size (n), the less important the shape of the distribution becomes, i.e. when n is very

16、 large the sampling distribution will be nearly normal regardless of the shape of the population distribution.Question 5The General Social Survey (GSS) is a sociological survey used to collect data on demographic characteristics and attitudes of residents of the United States. In 2010, the survey co

17、llected responses from over a thousand US residents. The survey is conducted face-to-face with an in-person interview of a randomly-selected sample of adults. One of the questions on the survey is “For how many days during the past 30 days was your mental health, which includes stress, depression, a

18、nd problems with emotions, not good?”Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010. Given this information, which of the following statements would be most appropriate to make regarding the true average number of days of “not g

19、ood” mental health in 2010 for US residents?Your AnswerScoreExplanationFor all US residents in 2010, there is a 95% probability that the true average number of days of “not good” mental health is between 3.40 and 4.24 days.For all US residents in 2010, based on this 95% confidence interval, we would

20、 reject a null hypothesis stating that the true average number of days of “not good” mental health is 5 days.There is not sufficient information to calculate the margin of error of this confidence interval.For these 1,151 residents in 2010, we are 95% confident that the average number of days of “no

21、t good” mental health is between 3.40 and 4.24 days.Inorrect0.00The confidence intervals only try to capture population parameters, not sample means. We can calculate exactly what the sample mean is.Total0.00 / 1.00Question ExplanationThis question refers to the following learning objective(s):Inter

22、pret a confidence interval as “We are XX% confident that the true population parameter is in this interval”, where XX% is the desired confidence level.Define margin of error as the distance required to travel in either direction away from the point estimate when constructing a confidence interval.Qu

23、estion 6A study suggests that the average college student spends 2 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a hypothesis test. You randomly sample 60 students from your dorm and find that on average they spen

24、t 3.5 hours a week communicating with others online. Which of the following is the correct set of hypotheses for this scenario?Your AnswerScoreExplanationH0:=2HA:2Correct1.00H0:=2HA:2H0:=3.5HA:3.5H0:x=2HA:x2Total1.00 / 1.00Question ExplanationThis question refers to the following learning objective(

25、s):Always construct hypotheses about population parameters (e.g. population mean, ) and not the sample statistics (e.g. sample mean, x). Note that the population parameter is unknown while the sample statistic is measured using the observed data and hence there is no point in hypothesizing about it.

26、Define the null value as the value the parameter is set to equal in the null hypothesis.Note that the alternative hypothesis might be one-sided ( the null value) or two-sided ( the null value), and the choice depends on the research question.Question 7Which of the following is the correct definition

27、 of the p-value?Your AnswerScoreExplanationP(observed or more extreme sample statistic | H0 true)P(H0 true)P(H0 true | HA false)P(H0 true | observed data)Inorrect0.00Review the associated learning objective. This sounds more like the posterior probability: P(hypothesis | data).Total0.00 / 1.00Questi

28、on ExplanationThis question refers to the following learning objective(s): Define a p-value as the conditional probability of obtaining a sample statistic at least as extreme as the one observed given that the null hypothesis is true. p-value = P(observed or more extreme sample statistic | H0 true)Q

29、uestion 8All but one of the following confidence intervals has a margin of error of 0.7. Which is the confidence interval with the different margin of error?Your AnswerScoreExplanation(4.7,3.3)(1.6,4.4)Correct1.00The width of a confidence interval is 2 times the margin of error, since we add and sub

30、tract the same margin of error to the sample statistics to obtain the bounds of the confidence interval. To solve this question we need to calculate the margin of error using this rule for each choice:|(1.64.4)/2|=1.4(20.3,21.7)(0.5,0.9)Total1.00 / 1.00Question ExplanationThis question refers to the

31、 following learning objective(s):Recognize that when the sample size increases we would expect the sampling variability to decrease.Define margin of error as the distance required to travel in either direction away from the point estimate when constructing a confidence interval, i.e. zSE.Question 9A researcher found a 2006 - 2010 survey showing that the average age of