ECON 262 Ch. 9

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

Do not reject Ho; we cannot conclude that the mean differs from zero

A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false.

FALSE

What is the decision rule when using the p-value approach to hypothesis testing?

Reject Ho if the p-value < α.

A Type I error is committed when we reject the null hypothesis, which is actually true.

TRUE

For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error.

TRUE

In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails.

TRUE

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The value of the test statistic is ____________.

z = -1.429

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350.To determine whether there has been a decrease in the average number of customers visiting the dealership daily, the appropriate hypotheses are _________.

Ho:μ≥800,HA:μ<800

Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type I error is often referred to as ___________.

a false positive

In general, the null and alternative hypotheses are __________.

mutually exclusive

A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the decision is to ________________________________________________.

reject Ho; we can conclude that the mean concentration of radon gas is greater than the safe level

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________________.

reject the null hypothesis

To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29 = 2.42 If we choose a 5% significance level, we _____________.

reject the null hypothesis and conclude that the mean IQ is greater than 100

When conducting a hypothesis test concerning the population mean, and the population standard deviation is known, the value of the test statistic is calculated as _________.

z=x−−μoσ/n√

On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis."

FALSE

The alternative hypothesis typically agrees with the status quo.

FALSE

Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim.

H0: p ≥ 0.84 and HA: p < 0.84

A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 6 minutes. A random sample of 40 employees were selected and they averaged 6.6 minutes. It is believed that the population standard deviation is 1.7 minutes. The α is set to 0.05. The p-value for this hypothesis test would be ______.

0.0128

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ______.

0.0957

A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error?

1%

Which of the following are two-tailed tests?

Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400

You want to test if more than 20% of homes in a neighborhood have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction. You take a sample of 60 homes from this neighborhood and find that 14 fit your criteria. The appropriate null and alternative hypotheses are _______________________.

Ho:p≤0.20,HA:p>0.20

Which of the following represents an appropriate set of hypotheses?

Ho:μ=0,HA:μ≠0

The null hypothesis typically corresponds to a presumed default state of nature.

TRUE

Under the assumption that the null hypothesis is true as an equality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample.

TRUE

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. In testing the politician's claim, how does one define the population parameter of interest?

The current proportion of babies born out of wedlock

A company has developed a new diet that it claims will lower one's weight by more than 10 pounds. Health officials decide to conduct a test to validate this claim. The consumers should be _____________________________________.

more concerned about Type I error

Consider the following competing hypotheses: Ho:μ = 0, HA:μ ≠ 0. The value of the test statistic is z = −1.38. If we choose a 5% significance level, then we ___________________________________________.

do not reject the null hypothesis and conclude that the population mean is not significantly different from zero

A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. The value of the test statistic is ___________.

t35 = 2.40

When conducting a hypothesis test concerning the population mean, and the population standard deviation is unknown, the value of the test statistic is calculated as __________.

tdf=x−−μos/n√

A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, Ho: μ ≥ 6 and HA: μ < 6, μ stand for _____________.

the mean delivery time