Question

ch 20* twenty - five adult citizens of the u.s. were asked to estimate the average income of all u.s. households. the mean estimate was $45,000 and a standard deviation of $15,000. (note: the actual average household income at the time of the study was about $68,000.) assume the 25 adults in the study can be considered an srs from the population of all adult citizens of the u.s. which of the following would cause the most worry about the validity of the confidence interval that you will calculate using this data?
a stemplot of the data shows a mild right - skew.
you do not know the population standard deviation \\( \sigma \\).
you notice that there is a clear outlier in the data.

question 11 1 pts
ch 21 which of the following procedures is not extremely sensitive to non - normal distributions?
the t test for matched pairs
the one - sample t test
the two - sample t test

Explanation:

• For the first question:
• A mild right - skew is not a major concern as the t - distribution (used for confidence intervals when population standard deviation is unknown) is somewhat robust to mild non - normality.
• When the population standard deviation \(\sigma\) is unknown, we use the sample standard deviation \(s\) and the t - distribution, which is a valid approach.
• An outlier can have a large impact on the mean and standard deviation (since both are non - resistant measures). It can distort the confidence interval calculation more significantly than the other two issues.
• For the second question:
• The one - sample t - test and two - sample t - test are more sensitive to non - normal distributions.
• The t - test for matched pairs (which is essentially a one - sample t - test on the differences) is relatively less sensitive compared to the other two when it comes to non - normal distributions, especially if the number of pairs is reasonably large.

Answer:

• First question: You notice that there is a clear outlier in the data.
• Second question: the t test for matched pairs