AP Statistics Unit 6

A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8, 12.3). Which of the following is the best interpretation of the interval?

• The probability is 0.95 that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.

• We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes.

• Ninety-five percent of the time the mean time for response is between 2.8 minutes and 12.3 minutes

• We are 95% confident that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.

An airline claims that the mean flight time between City X and City Y is 38 minutes. After taking many flights, a local business group believes that the claim is unrealistic and that the actual mean flight time is greater than 38 minutes. If the group conducts a study to investigate its belief, which of the following hypotheses should be tested?

• H₀ : x̄ = 38

  H_A : x̄ ≠ 38

• H₀ : x̄ = 38

  H_A : x̄ > 38

• H₀ : μ = 38

  H_A : μ ≠ 38

• H₀ : μ = 38

  H_A : μ > 38

A large city newspaper periodically reports the mean cost of dinner for two people at restaurants in the city. The newspaper staff will collect data from a random sample of restaurants in the city and estimate the mean price using a 90 percent confidence interval. In past years, the standard deviation has always been very close to $35. Assuming that the population standard deviation is $35, which of the following is the minimum sample size needed to obtain a margin of error of no more than $5 ?

• 90

• 112

• 133

• 147

A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses H0 : μ = 12 versus HA : μ < 12 was conducted, where μ represents the population mean number of ounces of the beverage dispensed by the machine. The p-value for the test was 0.08. Which of the following is the most appropriate conclusion to draw at the significance level of α = 0.05 ?

• Because the p-value is greater than the significance level, there is not convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.

• Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.

• Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

• Because the p-value is less than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Confidence Intervals: What is the formula for calculating a confidence interval for a population mean?

• x̄ * z * (σ/√n)

• x̄ ± z * (σ/√n)

• x̄ + z * (σ/√n)

• x̄ - z * (σ/√n)

Confidence Intervals: What is the margin of error in a confidence interval?

• It is a measure of the variability of the data and is calculated using the mean and the range.

• It is a measure of the accuracy of the estimate and is calculated using the standard error and the critical value.

• It is a measure of the confidence level and is calculated using the standard deviation and the sample size.

• It is a measure of the significance of the estimate and is calculated using the p-value and the z-score.

Confidence Intervals: What is the confidence level in a confidence interval?

• Probability that the interval contains the true population parameter

• The confidence level is the range of values within the interval

• The confidence level is the average of the upper and lower bounds of the interval

• The confidence level is the probability that the sample mean is within the interval

Confidence Intervals: How is the margin of error affected by the confidence level?

• The margin of error decreases

• The margin of error increases

• The margin of error remains the same

• The margin of error is not affected by the confidence level

Confidence Intervals: What is the interpretation of a 95% confidence level?

• There is a 95% chance that the true population parameter is within the interval

• 95% of the sample means will fall within the interval

• There is a 5% chance that the true population parameter is within the interval

• 95% of the population falls within the interval

What is a p-value in hypothesis testing?

• The probability of making a Type I error

• The probability of making a Type II error

• The probability of obtaining the observed data, or more extreme, if the null hypothesis is true

• The probability of obtaining the observed data, if the alternative hypothesis is true