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Effect of Outliers The following small data set represents
Chapter 5, Problem 50AYU(choose chapter or problem)
Problem 50AYU
Effect of Outliers The following small data set represents a simple random sample from a population whose mean is 50.
43 |
63 |
53 |
50 |
58 |
44 |
53 |
53 |
52 |
41 |
50 |
43 |
(a) A normal probability plot indicates that the data could come from a population that is normally distributed with no outliers. Compute a 95% confidence interval for this data set.
(b) Suppose that the observation, 41, is inadvertently entered into the computer as 14. Verify that this observation is an outlier.
(c) Construct a 95% confidence interval on the data set with the outlier. What effect does the outlier have on the confidence interval?
(d) Consider the following data set, which represents a simple random sample of size 36 from a population whose mean is 50. Verify that the sample mean for the large data set is the same as the sample mean for the small data set.
43 |
63 |
53 |
50 |
58 |
44 |
53 |
53 |
52 |
41 |
50 |
43 |
47 |
65 |
56 |
58 |
41 |
52 |
49 |
56 |
57 |
50 |
38 |
42 |
59 |
54 |
57 |
41 |
63 |
37 |
46 |
54 |
42 |
48 |
53 |
41 |
(e) Compute a 95% confidence interval for the large data set. Compare the results to part (a). What effect does increasing the sample size have on the confidence interval?
(f) Suppose that the last observation, 41, is inadvertently entered as 14. Verify that this observation is an outlier.
(g) Compute a 95% confidence interval for the large data set with the outlier. Compare the results to part (e). What effect does an outlier have on a confidence interval when the data set is large?
Questions & Answers
QUESTION:
Problem 50AYU
Effect of Outliers The following small data set represents a simple random sample from a population whose mean is 50.
43 |
63 |
53 |
50 |
58 |
44 |
53 |
53 |
52 |
41 |
50 |
43 |
(a) A normal probability plot indicates that the data could come from a population that is normally distributed with no outliers. Compute a 95% confidence interval for this data set.
(b) Suppose that the observation, 41, is inadvertently entered into the computer as 14. Verify that this observation is an outlier.
(c) Construct a 95% confidence interval on the data set with the outlier. What effect does the outlier have on the confidence interval?
(d) Consider the following data set, which represents a simple random sample of size 36 from a population whose mean is 50. Verify that the sample mean for the large data set is the same as the sample mean for the small data set.
43 |
63 |
53 |
50 |
58 |
44 |
53 |
53 |
52 |
41 |
50 |
43 |
47 |
65 |
56 |
58 |
41 |
52 |
49 |
56 |
57 |
50 |
38 |
42 |
59 |
54 |
57 |
41 |
63 |
37 |
46 |
54 |
42 |
48 |
53 |
41 |
(e) Compute a 95% confidence interval for the large data set. Compare the results to part (a). What effect does increasing the sample size have on the confidence interval?
(f) Suppose that the last observation, 41, is inadvertently entered as 14. Verify that this observation is an outlier.
(g) Compute a 95% confidence interval for the large data set with the outlier. Compare the results to part (e). What effect does an outlier have on a confidence interval when the data set is large?
ANSWER:Answer :
Step 1 :
Given, the following small data set represents a simple random sample from population whose mean is 50.
43 |
63 |
53 |
50 |
58 |
44 |
53 |
53 |
52 |
41 |
50 |
43 |
Mean = 50.25, std dev = 6.6 and n=12
a)
95% confidence interval for if the sample size n is 12.
Where, = 0.5 and
= 0.025, (n-1) degrees of freedom = 11
50.25
50.25 2.18 (1.905)
(46.1 , 54.4)
b) 14 is less than the lower fence,
14<Q1 - 1.5(IQR)
IQR = Q3 - Q1
= 53 - 43.5
= 9.5
Therefore, 43.5 - 1.5*9.5 = 29.5