Prob/Stats - Quiz 24

A newspaper in a small town asks an SRS of 250 citizens, “Do you favor a law banning lawn mowing after 8 pm?” Suppose that 35% of all citizens favor the law. If we took a very large number of SRSs of size n = 250 from this population, the sampling distribution of the sample proportion p-hat would have which of the following characteristics?

• Mean 0.35, standard deviation 0.03, shape unknown.

• Mean 0.30, standard deviation 0.03, approximately normal.

• Mean 0.30, standard deviation 0.03, shape unknown.

• Mean 0.35, standard deviation 0.03, approximately normal.

Thirty percent of the students at a high school participate in sports. A sample of students is to be selected in order to survey the students about their time spent on extracurricular activities. Which of the following sample sizes is the smallest that satisfies the large count condition to approximate the sampling distribution of p-hat as a normal distribution?

• 25

• 35

• 45

• 55

A newspaper decides to decrease the size of its random sample of citizens from 500 people to 250 people. The decrease in sample size will

• reduce the bias of the estimate

• increase the bias of the estimate

• reduce the variability of the estimate

• increase the variability of the estimate

The makers of Skittles claim that 20% of Skittles candy are orange. You select a random sample of 20 Skittles from a large bag. What can you tell deduce from this information.

• In a SRS of n=20, the sample proportion of orange Skittles will vary from the true proportion p =.4 by 1.79.

• In a SRS of n=20, the sample proportion of orange Skittles will vary from the true proportion p =.20 by 1.79.

• In a SRS of n=20, the sample proportion of orange Skittles will vary from the true proportion p =.4 by .089.

• In a SRS of n=20, the sample proportion of orange Skittles will vary from the true proportion p =.20 by .089.

Suppose 70% of all college women have been on a diet in the last 12 months. A sample survey interviews an SRS of 267 college women. Find the probability that 75% or more of the women in the sample have been on a diet.

• .037

• .499

• .967

• .073