# Question: The following small data set represents a simple random sample

The following small data set represents a simple random sample from a population whose mean is 50.
(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.
(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 in advertently 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?

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