"U.S. Teens Share Parents' Religion, Survey Finds" reported in 2005 that religious values were more important than they had been for teenagers in the 1960s. "God functions for most teenagers as a combination cosmic therapist and a divine butler . . . He is distant until you need him to solve a problem or make you feel better,"2 explained a University of North Carolina sociologist. In any case, the study found that 80% of teenagers reported they believed in God.
a. Find the mean and standard deviation of sample proportion believing in God for random samples of 64 teenagers.
b. Tell why the distribution's shape will be approximately normal.
c. Use the 68-95-99.7 Rule to sketch the distribution of sample proportion for samples of size 64 taken from a population where the proportion believing in God is 0.80.
d. If 48 in a sample of 64 teenagers report that they believe in God, is there reason to suspect that they are not a representative sample of all teenagers in terms of belief in God? Explain.
e. This exercise features two proportions: 0.80 and . Tell whether 0.80 plays the role of statistic or parameter.
f. How do we denote the number 0.80 in this context?
g. Tell whether 0.75 is a statistic or a parameter.
h. How do we denote the number 0.75 in this context?