Sample Final
统计数据分析代考 Suppose we are interested in the effffect of a high-quality mask on Covid infection risk. We recruit a group of 1,000 individuals for our study.
1.True/False If you know the relevant CDF, you can fully describe the random variable.
2.True/False The shortcomings of a convenience sample can be offffset with weighting techniques.
3.True/False The population mean, µ, is a random variable.
4.True/False A problem with the randomization protocol and non-compliance in an experiment are issues of external validity.
5.Does using a one-tailed test makes it harder to reject the null hypothesis? Does it change the probability of making a type I error?
6.Is the function below a valid PMF, PDF, CDF, or none of those things?
7.A recycling bin contains 6 coke cans, 2 diet coke cans, 5 coke bottles, and 5 diet coke bottles.
(a) What is the probability of pulling a diet coke container from the bin?
(b) What is the probability of pulling a diet coke container from the bin given that it is a can?
(c) What is the probability of pulling a can conditional on having drawn a single bottle (without replacement)?
(d) What is the probability of pulling a can conditional on having drawn a single bottle (with replacement)?
(e) Suppose that cans are worth $0.05 for their deposit and that bottles are worth $0.10 for their deposit. What is the expected value in deposits from pulling a single soda container from the bin?
8.Suppose a town has four quadrants: NE, NW, SE, and SW. The expected level of water contam-ination for households is 8 parts per million (ppm) for households in the NE quadrant, 6 ppm for households in the NW quadrant, 12 ppm for households in the SE quadrant, and 16 ppm for households in the SW quadrant. Within the town, 1,500 households live in the NE quadrant, 1,000 live in the NW quadrant, 500 live in the SE quadrant, and 2,000 live in the SW quadrant. What is the expected level of water contamination for a household in the town?
9.Bala, Baka, and Bama are preparing for fifinal exams. 统计数据分析代考
They want to attend the professor’s offiffiffice hours that are the least crowded. Bama is in Professor Moskowitz’s class and can never get out of the wait room for his afternoon offiffiffice hours. Baka is in Professor Frank’s class but his offiffiffice hours are canceled due to an internet outage. Bala is in Professor Lo’s class and claims that his offiffiffice hours are also always packed. Baka proposes a hypothesis test to determine if the mean attendance at Professor Lo’s and Professor Moskowitz’s offiffiffice hours are difffferent. What information do Baka and Bala need to test this hypothesis? Which formula should they use to calculate the test statistic?
10.Suppose you’re a member of the city council and you’re in charge of studying use of local roads by small and large capacity truckers. You are interested in the load size of trucks that use the primary roads in your town. There are 200 small-capacity trucks and 70 large-capacity trucks that use your town’s roads on a regular basis. You decide to stratify the sample. You sample 74 small-capacity trucks and 56 large-capacity trucks. Calculate the sampling weight, wL, you would use for the large-capacity trucks for your stratifified sample, and calculate the weight, wS, you would use for the small-capacity trucks?
11.Suppose, from a random sample of 1,040 residents of Chicago, 22% of residents had antibodies for Covid-19. Calculate a 95% confifidence interval for this estimate and provide a correct interpretation of it. Then calculate a 90% confifidence interval.
12.Consider Briar and Billie’s estimators for the population mean:
Determine whether each estimator is unbiased and consistent.
13.A researcher is interested in whether eating breakfast is associated with better performance on tests. She collected the data below and asked for your help analyzing it. Specififically, she wants to conduct a formal test as to whether the mean test score for breakfast-eaters is greater than the mean test score for breakfast-non-eaters.
(a) Which of the following is the most appropriate hypothesis test to use?
i.Chi-squared test
ii.Fisher’s exact test
iii. Two-sample z-test
iv.Two-sample t-test
v.One-sample z-test
vi.One-sample t-test
vii. Two-sample z-test 统计数据分析代考
viii. Paired t-test
ix.Welch’s two-sample t-test for unequal variances
x.Exact binomial test
(b) What are the null and alternative hypotheses?
(c) Does the alternative hypothesis imply a one-sided test, two-sided test, or are both equally appropriate?
(d) Using the hypothesis test you indicated in the question above, calculate the test statistic.
(e) Do you reject or fail to reject the null hypothesis at the α = 0.05 signifificance level?
14.Consider the results from a descriptive regression examining the relationship between absenteeism rates, party affiffiffiliation, and “ruralness” in a recent session of a state legislature. 统计数据分析代考
The absenteeism rate (absenteeism) indicates the proportion of roll-call votes that a legislator missed, so the variable= 0 for a legislator with perfect attendance, = 1 for a legislator who missed 100% of votes, and= 0.10 for a legislator who missed 10% of votes. The legislature only contains Democrats and Republicans, and the variable democrat is coded = 1 if the legislator is a Democrat and = 0 otherwise. Finally, the variable rural indicates the proportion of the district’s population residing in a rural area. For instance, rural is coded = 1 for a legislative district comprised entirely of rural residents, = 0 for a district comprised entirely of non-rural residents, and = 0.10 for a district comprised of 10% rural residents and 90% non-rural residents. Several legislators from both parties in the sample represent entirely rural and entirely non-rural districts. Make sure to indicate the appropriate units.
my.reg <- lm(absentee ~ democrat + rural, data = state.leg)
coef(my.reg)
## (Intercept) democrat rural
## .30 -0.05 0.10
(a) Calculate predicted values for the following:
i.A Republican representing a 100% rural district.
ii.A Republican representing a 10% rural district.
iii. A Democrat representing a 90% rural district:
iv.A Democrat representing a 0% rural district:
(b) Provide a correct interpretation of both estimated coeffiffifficients. 统计数据分析代考
(c) Provide a correct interpretation of the estimated intercept. Do we know if the intercept is substantively meaningful in this context?
(d) Can this regression tell us whether the relationship between rural and absentee varies by party affiffiffiliation? If not, indicate a single regression that would allow us to determine if the relationship varies by party.
15.Suppose we are interested in the effffect of a high-quality mask on Covid infection risk. We recruit a group of 1,000 individuals for our study. We randomly assign 500 to receive a weekly supply of N95 masks, and we randomly assign 500 to a control group that doesn’t receive free masks. At the conclusion of the study, our data indicate that 25 members of the N95 group had contracted Covid, and 50 members of the control group had contracted Covid. Suppose we further learn that, of those randomly assigned to the N95 group, 250 refused to wear an N95 (they claimed it was too uncomfortable). No one in the control wore an N95 mask during the period under study. Estimate the following quantities (if they are possible to estimate): the intent-to-treat effffect and the complier average treatment effffect.
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