For many years, the General Social Survey has asked respondents whether they favor the death penalty for persons convicted of murder. Support has been quite high in the United States, one of few Western nations that currently has the death penalty. The following figure uses the 20 General Social Surveys taken between 1975 and 2000 and plots the 95% confidence intervals for the population proportion in the United States who supported the death penalty in each of the 20 years of these surveys.

a. When we say we have €œ95% confidence€ in the interval for a particular year, what does this mean?
b. For 95% confidence intervals constructed using data for 20 years, let X = the number of the intervals that contain the true parameter values. Find the probability that x = 20, that is, all 20 inferences are correct.
c. Refer to part b. Find the mean of the probability distribution of X .
d. What could you do differently so it is more likely that all 20 inferences are correct?

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Unknown population proportion, which changes over time 0.60 0.70 1975 0.80 0.90 1976 1977 ー1978 ー1980 1982 1983 1984 1985 -1986 1987 1988 1989 1990 1991 -1993 1994 1996 -1998 -2000 -