Chapter 19 AP Statistics
Consider a one-sample two-sided z-test for a population proportion. Given that conditions for inference are met, which of the following is closest to the p-value for a test statistic of z=−1.86 ?
0.0628
A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known then what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college is
26.2% to 41.8%
Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. If the reported percent has a margin of error of 2.7 percentage points, which of the following is closest to the level of confidence?
90.0%
The proportion of detective widgets manufactured at The Gidget Widget Factory is not allowed to be over 4%. A corporate buyer wants to test whether the proportion of detective widgets exceeds the allowable proportion. He takes a random sample of widgets and finds that are defective. Find the correct interval in which the p-value fails.
Between 0.05 and 0.1
An online catalog company wants on-time delivery for at least 90% of the orders they ship. They have been shipping orders via UPS and FedEX, but will switch to a more expensive service (ShipFast) if there is evidence that this service can exceed the 90% on-time goal. As a test, the company sends a random sample of orders via ShipFast, and then makes follow up phone calls to see if these orders arrived on time. Which hypotheses should be tested?
Ho: p = 0.90 HA: p > 0.90
In order to make statistical inferences when testing a population proportion p, which of the following conditions verify that inference procedures are appropriate? The data are collected using a random sample or random assignment. The sample size is less than 10 percent of the population size. np0≥10 and n(1−p0)≥10 for sample size n and hypothesized proportion p0.
I, II, and III
Population - all cars; sample - 134 cars actually stopped at the checkpoint; p - proportion of all cars with safety problems; pˆ - proportion of cars in the sample that actually have safety problems (10.4%).
Plausible Independence condition: There is no reason to believe that the safety problems of cars are related to each other. Randomization condition: This sample is not random, so hopefully the cars stopped are representative of cars in the area. 10% condition: The 134 cars stopped represent a small fraction of all cars, certainly less than 10%. Success/Failure condition: npˆ = 14 and nqˆ= 120 are both greater than 10, so the sample is large enough. A one-proportion z-interval can be created for the proportion of all cars in the area with safety problems.
A one-sample z-test for a population proportion will be conducted using a simple random sample selected without replacement from a population. Which of the following is a check for independence?
The population size is more than 10 times the sample size.
A company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H0:p=0.08 versus Ha:p>0.08 at the significance level of α=0.01. The test yielded a p-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion?
The pp-value is less than αα, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
On the day before an election in a large city, each person in a random sample of 1,000 likely voters is asked which candidate he or she plans to vote for. Of the people in the sample, 55 percent say they will vote for candidate Taylor. A margin of error of 3 percentage points is calculated. Which of the following statements is appropriate?
The sample proportion minus the margin of error is greater than 0.50, which provides evidence that more than half of all likely voters plan to vote for candidate Taylor.
Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control officer at the plant periodically tests the machines to be sure that the bottles are filled to an appropriate amount. The null hypothesis of the test is that the mean is at least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces. Which of the following describes a Type I error that could result from the test?
The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces.
The representatives from the Department of Labor want to estimate a percentage of females in the United States labor force to within ±5%, with 90% confidence. How many employment records should they sample?
They should sample at least 269 employment records.
A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation of the 95 percent confidence level?
We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.
Bank officers are considering targeting young parents with an offer to start a college savings plan. They have decided to pursue this new marketing program only if at least 25 percent of such parents might be interested in this type of plan. The program surveyed 300 randomly selected parents, or whom 32 percent indicated some interest. A hypothesis test will be used to determine whether the data provide convincing statistical evidence that more than 25 percent of parents would be interested in the savings plan. Which of the following is the test statistic for the appropriate test?
z=(..32-.25)/(.25*.75/300)^.5
