10.2 Warm Up

After a tropical storm in a certain state, news reports indicated that 19 percent of households in the state lost power during the storm. A state engineer believes that estimate is too low. The engineer will collect data to perform a hypothesis test on the proportion of all households without power. Which of the following are the appropriate hypotheses for such a test?

• H0 : p̂ = 0.19, Ha : p̂ < 0.19

• H0 : p̂ = 0.19, Ha : p̂ > 0.19

• H0 : p = 0.19, Ha : p < 0.19

• H0 : p = 0.19, Ha : p ≠ 0.19

• H0 : p = 0.19, Ha : p > 0.19

Let random variable R represent the the number of visitors to a certain museum during a given day. The following table shows the probability distribution of the random variable. Which of the following claims about the distribution of random variable R is best supported by the histogram?

• The most likely number of visitors to the museum on a given day is between 450 and 500.

• The mean number of visitors to the museum is much less than the median number of visitors.

• The mean number of visitors to the museum is much greater than the median number of visitors.

• On a given day, the number of visitors from 100 through 500 will occur with equal probabilities.

• On a given day, it is equally likely for the museum to have less than 300 visitors as it is to have more than 300 visitors.

For a population of leghorn chickens, the mean number of eggs laid per chicken is 0.70 with standard deviation 0.20 egg. For a population of Sussex chickens, the mean number of eggs laid per chicken is 0.50 with standard deviation 0.10 egg. Two independent random samples of chickens were taken from the populations. The following table shows the sample statistics. Mike claims that for all samples of size 36 from the population of leghorn chickens and all samples of size 36 from the population of Sussex chickens, the mean of all possible differences in sample means (leghorn minus Sussex) is 0.30 eggs per chicken. Is Mike’s claim correct?

• Yes. The mean is 0.75 − 0.45 = 0.30 egg per chicken.

• No. The mean is 0.30 − 0.12 = 0.18 egg per chicken.

• No. The mean is 0.70 − 0.50 = 0.20 egg per chicken.

• No. The mean is 0.20 − 0.10 = 0.10 egg per chicken.

• No. The mean is 36(0.75) − 36(0.45) = 10.8 eggs per chicken.

Environmentalists want to estimate the percent of trees in a large forest that are infested with a certain beetle. The environmentalists will select a random sample of trees to inspect. Which of the following is the most appropriate method for creating such an estimate?

• A two-sample z-interval for a population proportion

• A one-sample z-interval for a sample proportion

• A one-sample z-interval for a population proportion

• A two-sample z-interval for a difference between sample proportions

• A two-sample z-interval for a difference between population proportions

A recent study on the way that people talk indicated, with 95 percent confidence, that between 35 percent and 41 percent of all adults find the word “whatever” to be the most annoying word in conversation. Based on the confidence interval, which of the following claims is supported?

• Less than 25 percent of all adults find the word “whatever” to be the most annoying word in conversation.

• More than 30 percent of all adults find the word “whatever” to be the most annoying word in conversation.

• More than 45 percent of all adults find the word “whatever” to be the most annoying word in conversation.

• More than half of all adults find the word “whatever” to be the most annoying word in conversation.

• At least 95 percent of all adults find the word “whatever” to be the most annoying word in conversation.