AP Stats Significant Tests

• 90% confidence

• 93% confidence

• 95% confidence

• 98% confidence

• 99% confidence

A researcher has conducted a survey using a simple random sample of 50 registered voters to create a confidence interval to estimate the proportion of registered voters favoring the election of a certain candidate for mayor. Assume that a sample proportion does not change. Which of the following best describes the anticipated effect on the width of the confidence interval if the researcher were to survey a random sample of 200, rather than 50, registered voters?

• The width of the new interval would be about one-fourth the width of the original interval.

• The width of the new interval would be about one-half the width of the original interval.

• The width of the new interval would be about the same width as the original interval.

• The width of the new interval would be about twice the width of the original interval.

• The width of the new interval would be about four times the width of the original interval.

An independent research firm conducted a study of 100 randomly selected children who were participating in a program advertised to improve mathematics skills. The results showed no statistically significant improvement in mathematics skills, using a = 0.05. The program sponsors complained that the study had insufficient statistical power. Assuming that the program is effective, which of the following would be an appropriate method for increasing power in this context.

• Use a two-sided test instead of a one-sided test.

• Use a one-sided test instead of a two-sided test.

• Use a = 0.01 instead of a = 0.05.

• Decrease the sample size to 50 children.

• Increase the sample size to 200 children.

A planning board in Elm County is interested in estimating the proportion of its residents that are in favor of offering incentives to high-tech industries to build plants in that county. A random sample of Elm County residents was selected. All of the selected residents were asked, "Are you in favor of offering incentives to high-tech industries to build plants in your county?" A 95 percent confidence interval for the proportion of residents in favor of offering incentives was calculated to be 0.54 ± 0.05. Which of the following statements is correct?

• At the 95% confidence level, the estimate of 0.54 is within 0.05 of the true proportion of county residents in favor of offering incentives to high-tech industries to build plants in the county.

• At the 95% confidence level, the majority of area residents are in favor of offering incentives to high-tech industries to build plants in the county.

• In repeated sampling, 95% of sample proportions will fall in the interval (0.49, 0.59)

• In repeated sampling, the true proportion of county residents in favor of offering incentives to high-tech industries to build plants in the county will fall in the interval (0.49, 0.59).

• In repeated sampling, 95% of the time the true proportion of county residents in favor of offering incentives to high-tech industries to build plants in the county will be equal to 0.54.

• (A) I only

• (B) I and II only

• (C) I and III only

• (D) II and III only

• (E) I, II, and III

• (A) The mean weight of baseball players is not significantly lower than the mean weight of hockey players at the 0.05 level.

• (B) The mean weight of baseball players is not significantly lower than the mean weight of hockey players at the 0.10 level.

• (C) The mean weight of baseball players is significantly higher than the mean weight of hockey players at the 0.10 level.

• (D) The mean weight of baseball players is significantly lower than the mean weight of hockey players at the 0.05 level.

• (E) The mean weight of baseball players is significantly different from the mean weight of hockey players at the 0.05 level.

About 76% of college professors said that if they could pick a career over again, they would choose to be a professor again. A random sample of 59 college professors in Colorado showed that 47 claim they would choose college teaching again. Does this indicate the proportion of professors in Colorado who would choose the career again is greater than the national rate of 76%? Use a 1% level of significance. 

• Do not reject H₀ (z = 0.76)

• Reject H₀ (z = 1.45)

• Do not reject H₀ (z = 1.45)

• Reject H₀ (z = 0.6)

Identify the correct null hypothesis:

• H₀: p = 0.50

• H₀: µ = 100

• H₀: p = 0.48

• H₀: µ = 96

We conclude "Fail to reject H₀". What could we use as our interpretation?

• The proportion of babies born male is not 0.50.

• There is not enough evidence to say that the proportion of babies born male is different from 0.50.

• There is not enough evidence to say that the proportion of babies born male is 0.50.

• A
• B
• C
• D