a) Compute the sample mean of each data set. Calculate the sample mean for data
ID: 3274825 • Letter: A
Question
a) Compute the sample mean of each data set.
Calculate the sample mean for data set I.
x overbar
equals98.29
(Type an integer or a decimal.)
Calculate the sample mean for data set II.
x overbar
equals99.82
(Type an integer or a decimal.)
Calculate the sample mean for data set III.
x overbar
equals99.46
(Round to three decimal places as needed.)
(b) For each data set, construct a 95% confidence interval about the population mean.
A 95% confidence interval for data set I is
(Use ascending order. Round to two decimal places as needed.)
A 95% confidence interval for data set II is
(Use ascending order. Round to two decimal places as needed.)
A 95% confidence interval for data set III is
(Use ascending order. Round to two decimal places as needed.)
(c) What impact does the sample size n have on the width of the interval?
A.As the sample size increases, the width of the interval decreases.
B.As the sample size increases, the width of the interval increases.
C.The sample size has no impact on the width of the interval.
(d) Suppose that the data value 106 was accidentally recorded as 061. For each data set, construct a 95% confidence interval using the misentered data.
A 95% confidence interval for data set I is (nothing,nothing).
(Use ascending order. Round to two decimal places as needed.)
The 95% confidence interval for data set II is (nothing,nothing).
(Use ascending order. Round to two decimal places as needed.)
The 95% confidence interval for data set III is
(Use ascending order. Round to two decimal places as needed.)
(e) Which intervals, if any, still capture the population mean,100?
A.Only set III
B.Sets I and II
C.All of the sets
D.Sets II and III
E.Sets I and III
F.Only set II
G.Only set I
H.None of the sets
Which of the following is the concept illustrated with the misentered data?
A.The procedure for constructing the confidence interval is not robust. The smaller the sample size, the less resistant the mean. Therefore, the confidence interval is more robust.
B.The procedure for constructing the confidence interval is robust. The larger the sample size, the more resistant the mean. Therefore, the confidence interval is less robust.
C.The procedure for constructing the confidence interval is robust. The larger the sample size, the more resistant the mean. Therefore, the confidence interval is more robust.
Data_Set_III Data_Set_II Data_Set_I 106 106 106 122 122 122 93 93 93 127 127 127 86 86 86 77 77 77 74 74 74 109 109 109 88 88 91 91 111 111 83 83 113 113 115 115 100 100 125 125 97 97 86 86 84 84 101 101 91 109 115 94 100 82 84 107 94 113Explanation / Answer
Solution:
a)Sample mean
Data_Set_I = 99.25
Data_Set_II = 99.40
Data_Set_III = 99.23
b)95% CI
Data_Set_I = (83.94,114.56)
Data_Set_II = (92.09,106.70)
Data_Set_III = (93.9,104.57)
c) As the sample size increases, the width of the interval decreases.
d) 95% CI when 106 replace by 061
Data_Set_I = (75.38,111.87)
Data_Set_II = (88.91,105.39)
Data_Set_III = (91.84,103.62)
Done.
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