November 6, 2012 was election day. Many of the major television networks aired c
ID: 3224435 • Letter: N
Question
November 6, 2012 was election day. Many of the major television networks aired coverage of the incoming election results during the primetime hours. The provided table displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults.
123
120
45
30
40
86
36
52
86
2
70
155
70
168
156
107
126
66
71
97
73
90
69
5
68
A. What is the population parameter of interest? Define using the appropriate notation. _____________ ________________________________________________ B. Use the data from the sample to estimate the parameter of interest. Report your answer with two decimal places. _____________
C. Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples? ________________________________________________________________
E. Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error. ________________________________________________________________
F. Use the estimate of the standard error to construct a 95% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Use three decimal places in your answer.
G. Use the percentiles of your bootstrap distribution to provide a 92% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Indicate which percentiles you are using.
H. Interpret your 92% confidence interval in the context of this data situation. ________________________________________________________________
123
120
45
30
40
86
36
52
86
2
70
155
70
168
156
107
126
66
71
97
73
90
69
5
68
Explanation / Answer
Part A
Solution:
The population parameter of interest is the amount of average time (µ) in minutes spent watching election coverage.
Part B
Solution:
The estimated parameter of interest or the estimate for the population average time µ in minutes is given as sample mean = Xbar = 80.44.
Part C
Solution:
For construction of a bootstrap distribution, we will consider the original sample as the population. For the given sample, the size is given as 25 and we will also take the random samples of size 25 for the sampling distribution. We will treat the sample as a population and we will draw large number of samples with size 25 with replacement. We will use the excel functions such as =randbetween(a,b) or =index(range, randbetween(a,b)) for bootstrap of a distribution.
Part E
Solution:
About 1000 samples are drawn from the population distribution with the parameters same as the given original sample. We use excel to construct the bootstrap distribution. From the given bootstrapping we get
Standard error = SD/sqrt(n) = 39.59044/sqrt(25) = 7.693869
Part F
Solution:
Here, we have to find out the 95% confidence interval for the population mean.
Sample size = n = 25
Degrees of freedom = n – 1 = 24
Critical value = t = 2.0639
Estimate for mean = 71.57625
Standard error = SE = 7.693869
Confidence interval = Mean -/+ t*SE
Confidence interval = 71.57625 -/+ 2.0639*7.693869
Lower limit = 71.57625 - 2.0639*7.693869 = 55.69687
Upper limit = 71.57625 + 2.0639*7.693869 = 87.45563
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