數(shù)據(jù)分析3(2)

1、question 1 suppose we are interested in studying how much chocolate is consumed by coursera students, measured in grams per week. after surveying 500 students, we calculate an average of 175 grams per week with a standard deviation of 195 grams per week. which of the following is not necessarily tru

2、e? your answer score explanation a histogram of the samples will be skewed to the right. x=175,s=195=175, =195correct1.00 just because the sample statistics are thevalues will be exactly equal to them, ther=175, =195. a point estimate for the population standard deviation is 195. total 1.00 / 1.00 q

3、uestion 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 2 r

4、esearchers 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 let s assume they are - then the sample mean

5、is 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 answer score explanation mean squared error = 0.105 standard error =

6、 0.019 standard deviation = 0.019 standard deviation = 0.417 inorrect0.00 we quantify variability in the sample mean by calmean) se=/n. standard error = 0.417 total 0.00 / 1.00 question explanationthis question refers to the following learning objective(s): calculate the sampling variability of the

7、mean, the standard error, as se= /n. question 3 students are asked to count the number of chocolate chips in 22 cookies for a class activity. they found that the cookies on average had 14.77 chocolate chips with a standard deviation of 4.37 chocolate chips. after collecting the data, a student repor

8、ts the standard error of the mean to be 0.93 chocolate chips. what is the bestway to interpret the students result? your answer score explanation 0.93 chocolate chips is a measure of the variability wed expect in calculations of the mean number of chocolate chips if we took repeated random samples o

9、f 22 cookies. the student either made a calculation error or his result is meaningless, because it does not make sense to talk about 0.93 chocolate chips. inorrect0.00 standard error meestimates from diffrom the same povariability. 0.93 is the standard deviation of the number of chocolate chips in a

10、 chocolate chip cookie. 0.93 chocolate chips is a measure of the variability in the mean number of chocolate chips across all chocolate chip cookies. total 0.00 / 1.00 question explanationthis question refers to the following learning objective(s): distinguish standard deviation (or s) and standard

11、error (se): standard deviation measures the variability in the data, while 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 4 which of the following is false about the cen

12、tral limit theorem (clt)? your answer if we take more samples from the original population, the sampling distribution is more likely to be nearly normal. if the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. as the

13、sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution. inorrectthe clt states that the sampling distribution will be centered at the true population parameter. total question explanationthis qu

14、estion refers 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 suff

15、iciently 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 e

16、rror of n.x n(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. w

17、hen n is very large the sampling distribution will be nearly normal regardless of the shape of the population distribution. question 5 to get an estimate of consumer spending in the u.s. following the thanksgiving holiday, 436 randomly sampled american adults were surveyed. their daily spending for

18、the six-day period following thanksgiving averaged $84.71. a 95% confidence interval based on this sample is ($80.31, $89.11). which of the following are true? we are 95% confident that the average spending of the 436 american adults in this sample is between $80.31 and $89.11. if we collected many

19、random samples of the same size and calculated a confidence interval for daily spending for each sample, then we would expect 95% of the intervals to contain the true population parameter. we are 95% confident that the average spending of all american adults is between $80.31 and $89.11. your answer

20、 score exi and ii i and iii ii and iii i, ii, and iii none inorrect0.00 sototal 0.00 / 1.00 question explanationthis question refers to the following learning objective(s): interpret a confidence interval as “we are xx% confident that the true population parameter is in this interval”, where xx% is

21、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. question 6 an insurance company is reviewing its current policy rates. when originally setting the rates they believed tha

22、t the average claim amount was $1,800. they are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. they randomly select 40 claims, which yield a sample mean of $1,950. which of the following is the correct set of hypotheses for this scenari

23、o? your answer score h0:=1,800ha:1,800correct1.00 h0:=1,950ha:1,800h0:=1,800ha:1,950h0:x=1,800ha:x1,800total 1.00 / 1.00 question explanationthis question refers to the following learning objective(s): always construct hypotheses about population parameters (e.g. population mean, ) and not the sampl

24、e 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. define the null value as the value the parameter is set to equal in the null hypothesis. note that t

25、he alternative hypothesis might be one-sided (the null value) or two-sided ( the null value), and the choice depends on the research question. question 7 which of the following is the correct definition of the p-value? your answer score explanation p(h0 true) p(h0 true | observed data) p(observed or

26、 more extreme sample statistic | h0 true) correct1.00 define a p-value as the conditional probabileast as extreme as the one observed givenp(h0 true | ha false) total 1.00 / 1.00 question explanationthis question refers to the following learning objective(s): define a p-value as the conditional prob

27、ability 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) question 8 suppose we collected a sample of size n = 100 from some population and used the data to calculate a 95%

28、confidence interval for the population mean. now suppose we are going to increase the sample size to n= 300. keeping all else constant, which of the following would we expect to occur as a result of increasing the sample size? the standard error would decrease. width of the 95% confidence interval w

29、ould increase. the margin of error would decrease. your answer score explanation ii and iii i and iii correct1.00 increasing the sample size (while keeping the same confidence lewhich decreases the margin of error and hence the width of interi and ii i, ii, and iii none total 1.00 / 1.00 question ex

30、planationthis question refers to the 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 con

31、fidence interval, i.e. z?se. question 9 a researcher found a 2006 - 2010 survey showing that the average age of women at first marriage is 23.44. suppose a researcher believes that this value may have increased more recently, but as a good scientist he also wants to consider the possibility that the

32、 average age may have decreased. the researcher has set up his hypothesis test; which of the following states the appropriate ha correctly? your answer score explanation ha:=23.44 years old. inorrect0.00 because the researcher is interested in both an intwo-sided. ha:23.44 years old. ha:23.44years o

33、ld. total 0.00 / 1.00 question explanationthis question refers to the following learning objective(s): 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 10 you set up a two-sided hypothes

34、is test for a population mean with a null hypothesis of h0:=100. you chose a significance level of =0.05. the p-value calculated from the data is 0.12, and hence you failed to reject the null hypothesis. suppose that after your analysis was completed and published, an expert informed you that the tr

35、ue value of is 104. how would you describe the result of your analysis? your answer score explanation a type 1 error was made because you failed to reject the null hypothesis but is really not equal to 100. you did not make a type 1 or type 2 error. a type 2 error was made because you failed to reje

36、ct the null hypothesis but is really not equal to 100. correct1.00 type 2 error is mto be rejected wtotal 1.00 / 1.00 question explanationthis question refers to the following learning objective(s): note that the conclusion of a hypothesis test might be erroneous regardless of the decision we make.

37、define a type 1 error as rejecting the null hypothesis when the null hypothesis is actually true. define a type 2 error as failing to reject the null hypothesis when the alternative hypothesis is actually true. question 11 a statistician is studying blood pressure levels of italians in the age range

38、 75-80. the following is some information about her study: the data were collected by responses to a survey conducted by email, and no measures were taken to get information from those who did not respond to the initial survey email. the sample observations only make up about 4% of the population. t

39、he sample size is 2,047. the distribution of sample observations is skewed - the skew is easy to see, although not very extreme. the researcher is ready to use the central limit theorem (clt) in the main part of her analysis. which aspect of the her study is most likely to prevent her from using the

40、 clt? your answer score explanation (i), because the sample may not be random and hence observations may not be independent. correct1.00 the correct answer is that the data arose ascollection would likely result in a sample whitalians aged 75-80, which would violate thcondition necessary for the clt

41、. (ii), because she only has data from a small proportion of the whole population. (iii), because the sample size is too small compared to all italians in the age range 75-80. (iv), because there is some skew in the sample distribution. total 1.00 / 1.00 question explanationthis question refers to t

42、he 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 large (n

43、30 or larger if the data are considerably 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

44、n:x n(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

45、 very large the sampling distribution will be nearly normal regardless of the shape of the population distribution. if the conditions necessary for the clt to hold are not met, note this and do not go forward with the analysis. (we will later learn about methods to use in these situations.) question

46、 12 sat scores are distributed with a mean of 1,500 and a standard deviation of 300. you are interested in estimating the average sat score of first year students at your college. if you would like to limit the margin of error of your 95% confidence interval to 25 points, at least how many students

47、should you sample? your answer score explanation 392 553 inorrect0.00 me=z?sn25=1.96300nn=1.9623002252n=553.19rounding down would result in a slightly larger margin of error than554 13,830 393 total 0.00 / 1.00 question explanationthis question refers to the following learning objective(s): calculat

48、e the required sample size to obtain a given margin of error at a given confidence level by working backwards from the given margin of error. question 13 true / false: decreasing the significance level () will increase the probability of making a type 1 error. your answer score explanation true inor

49、rect0.00 note that the probability of making a type 1 error is equivalenthypothesis is true. false total 0.00 / 1.00 question explanationthis question refers to the following learning objective(s): note that the probability of making a type 1 error is equivalent to the significance level when the nu

50、ll hypothesis is true, and choose a significance level depending on the risks associated with type 1 and type 2 errors. use a smaller if type 1 error is relatively riskier. use a larger if type 2 error is relatively riskier. question 14 the nutrition label on a bag of potato chips says that a one ou

51、nce (28 gram) serving of potato chips has 130 calories and contains ten grams of fat, with three grams of saturated fat. a random sample of 35 bags yielded a sample mean of 134 calories with a standard deviation of 17 calories. we are evaluating whether these data provide convincing evidence that th

52、e nutrition label does not provide an accurate measure of calories in the bags of potato chips at the 10% significance level. which of the following is correct? your answer score explanation the p-value is approximately 8%, which means we should fail to reject the null hypothesis and determine that

53、these data do notprovide convincing evidence the nutrition label does not provide an accurate measure of calories in the bags of potato chips. the p-value is approximately 16%, which means we should fail to reject the null hypothesis and determine that these data do notprovide convincing evidence th

54、e nutrition label does not provide an accurate measure of calories in the bags of potato chips. correct1.00 h0:=zp-value=134-1301=130)=p(z1.39)=210%, fail to reject h0. the p-value is approximately 16%, which means we should reject the null hypothesis and determine that these data provide convincing evidence the nutrition label does not provide an accurate measure of calories in the bags of potato chips. the p-value is approximately 8%, which means we should reject the null hypothesis and determine that these data provide convincing evidence the nutrit