9.2 Warm Up STATS 02.18.25

Which of the following is not a condition for constructing a confidence interval to estimate the difference between two population proportions?

• The samples must be selected randomly.

• The data must come from populations with approximately normal distributions.

• When samples are taken without replacement, each population must be at least 10 times as large as its corresponding sample.

• The samples must be independent of each other.

• The observed number of successes and failures for both samples must be at least 10.

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CCSS.HSS.IC.B.4

A random sample of residents in city J were surveyed about whether they supported raising taxes to increase bus service for the city. From the results, a 95 percent confidence interval was constructed to estimate the proportion of people in the city who support the increase. The interval was (0.46, 0.52). Based on the confidence interval, which of the following claims is supported?

• More than 90 percent of the residents support the increase.

• More than 60 percent of the residents support the increase.

• More than 40 percent of the residents support the increase.

• Fewer than 10 percent of the residents support the increase.

• Fewer than 25 percent of the residents support the increase.

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CCSS.HSS.IC.B.4

• Days

• Dollars

• Companies

• Workers

• There are no units associated with the mean of the sampling distribution.

At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of D are 2.6 doughnuts and 3.6 (doughnuts)², respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of ?Which of the following is the standard deviation, in dollars, of the probability distribution of P?

A city planner wants to estimate the proportion of city residents who commute to work by subway each day. A random sample of 30 city residents was selected, and 28 of those selected indicated that they rode the subway to work. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?

• No, because the size of the population is not known.

• No, because the sample is not large enough to satisfy the normality conditions.

• Yes, because the sample is large enough to satisfy the normality conditions.

• Yes, because the sample was selected at random.

• Yes, because sampling distributions of proportions are modeled with a normal model.