ORMS 3310 Module 9

The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest?

A) The mean score on the eighth-grade reading comprehension test

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) a false positive

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

B) Reject Ho if the p-value < α.

The alternative hypothesis typically ________.

B) contests the status quo, for which a corrective action may be required

If the p-value for a hypothesis test is 0.07 and the allowed probability of making a Type I error is 0.05, then the correct decision is to ________.

B) not reject the null hypothesis

The null hypothesis in a hypothesis test refers to ________.

B) the default state of nature or status quo

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is ________.

B) z = 1.50

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?

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

A Type II error occurs when we ________.

D) do not reject the null hypothesis when it is actually false

In general, the null and alternative hypotheses are ________.

D) mutually exclusive

A(n) ________ error is committed when we reject the null hypothesis when the null hypothesis is actually true.

Type I

We define the allowed probability of making a Type I error as α, and we refer to 100α% as the ________.

significance level

Given the ________ of the z distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.

symmetry

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 null and alternative hypotheses?

A) H0 : p ≤ 0.50 and HA : p > 0.50

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?

A) The current proportion of babies born out of wedlock

For a given sample size n, ________.

A) decreasing the probability of a Type I error α will increase the probability of a Type II error β

A Type I error occurs when we ________.

A) reject the null hypothesis when it is actually true

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ________.

A) the mean GPA of all university honors students

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 ________.

A) the mean delivery time

If the null hypothesis is rejected at a 1% significance level, then ________.

A) the null hypothesis will be rejected at a 5% significance level

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, what is the correct decision and conclusion?

D) Do not reject the null hypothesis; we cannot conclude that the population mean is significantly different from zero.

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

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 ________.

A) 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. At the 5% significance level, what is your decision and conclusion?

D) Do not reject Ho; we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. At a 5% significance level, what is your decision and conclusion?

D) Do not reject; Ho we cannot conclude that the mean GPA is significantly greater than 3.50

It is generally believed that at least 0.50 of all babies in a large city in California are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is in fact decreasing. Identify the correct null and alternative hypotheses to test the politician's claim

D) H0: p ≥ 0.50 and HA: p < 0.50

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.

D) H0: p ≥ 0.84 and HA: p < 0.84

Which of the following types of tests may be performed?

D) Right-tailed, left-tailed, and two-tailed tests

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

TRUE

A hypothesis test regarding the population mean μ is based on the sampling distribution of the sample mean X.

TRUE

As a general guideline, we use the alternative hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required.

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 null hypothesis typically corresponds to a presumed default state of nature or status quo.

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

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 - muo) / (s/square root n)

If we reject a null hypothesis at the 1% significance level, then we have ________ evidence that the null hypothesis is false.

very strong

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 - muo) / (standard deviation/square root n)