ISDS 2000 EXAM 3

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 $16,000. A random sample of 35 students had an average debt load of $17,200. It is believed that the population standard deviation for student debt load is $4,370. The α is set to 0.05. The p-value for this hypothesis test would be __________.

0.105

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 9 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 23 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 9.8 pounds with a standard deviation of 2.0 pounds. The test statistic for this hypothesis would be __________.

0.92

In general, we follow three steps when formulating the competing hypotheses. Place these steps in the correct sequence.

1. Identify the population parameter of interest. 2. Determine whether it is a one-tailed or two-tailed test. 3. Include some form of the equality sign in the null hypothesis.

In hypothesis testing, two incorrect decisions are possible:

Reject the null hypothesis when it is true. Do not reject the null hypothesis when it is false.

True or False. 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

True or false: In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.

True

Rejecting the null hypothesis when the null hypothesis is true.

Type I error

The alternative hypothesis typically _____

contests the status quo and may suggest a corrective action if true.

The -------- approach to hypothesis testing is attractive when a computer is unavailable and all calculations must be done by hand.

critical value

Consider the following competing hypotheses: H0: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

HA: μ< μ0

left tailed alternative hypothesis

H0: μ>= μ0

left tailed null hypothesis

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

A binomial distribution can be approximated by a ------distribution for large sample sizes.

normal

The normal distribution approximation for a binomial distribution is valid when

np ≥ 5 and n(1 - p) ≥ 5

As a point estimate of the population proportion, we calculate ______.

p (line)

The two equivalent methods to solve a hypothesis test are the

p-value approach. critical value approach

In hypothesis testing, the standard error of the sample proportion P is computed as

po(1−po)/n√

μ

population mean

HA: μ> μ0

right tailed alternative hypothesis

H0: μ<= μ0

right tailed null hypothesis

When testing μ and σ is known, H0 can never be rejected if z ≤ 0 for a

right-tailed test.

If the population standard deviation is unknown, it can be estimated by using ______.

s

When performing a hypothesis test on μ when the value of σ is unknown, the test statistic is computed as x−μ0s/√n and it follows the

tdf distribution with (n - 1) degrees of freedom.

HA: μ/= μ0

two tailed test alternative hypothesis

If the underlying population is not normally distributed, we need the sample size to be at least

30

Rejecting a false null hypothesis.

Correct decision

Which of the following is NOT a step in the p-value approach to hypothesis testing?

Graph the distribution of the sample data.

null hypothesis

H0= μ= μ0

alternative hypothesis

HA= μ/= μ0

Not rejecting the null hypothesis when the null hypothesis is false.

Type II error

μ0

hypothesized population mean

By reducing the likelihood of a Type I error, we ------- the likelihood of a Type II error,

increase

E(P line)=

p

H0: μ= μ0

two tailed null hypothesis

The p-value approach to hypothesis testing has--- steps

4

Specify the competing hypotheses that would be used in order to determine whether the population mean is less than 150.

H0: μ ≥ 150 and HA: μ < 150

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement—students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes. Which of the following can be used to determine whether the schedule adjustment reduced the average lateness time of 12 minutes?

H0:μ≥12,HA:μ<12H0:μ≥12,HA:μ<12

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 __________.

H0:μ≥800,HA:μ<800H0:μ≥800,HA:μ<800

Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200. Which of the following hypothesis tests should be performed?

Left-tailed

An important final conclusion to a statistical test is to...

clearly interpret the results in terms of the initial claim.

The expected value of the sampling distribution of P (line) is the

population parameter

Unlike the mean and standard deviation, the population proportion p is a descriptive summary measure that can be used for data that are

qualitative / categorical

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. At a 5% significance level, the decision is to __________.

reject H0; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20

A Type I error occurs when we...

reject the null hypothesis when it is actually true.

In hypothesis testing, if the sample data provide significant evidence that the null hypothesis is incorrect, then we

reject the null hypothesis.

If the chosen significance level is α = 0.05, then there is a 5% chance of

rejecting a true null hypothesis.

We use hypothesis testing to

resolve conflicts between two competing opinions

A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team's previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach's claim. He takes a sample of 36 of the team's games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is the value of the appropriate test statistic to test the new coach's claim at the 1% significance level?

t35 = 2.00

A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 7 pCi/L. The school samples the air for 36 days and finds an average concentration of 7.4 pCi/L with a standard deviation of 1 pCi/L. The value of the test statistic is __________.

t35 = 2.40

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. If the advisor tests the hypotheses H0: μ ≤ 300 versus HA: μ > 300, μ stands for __________.

the average number of automobiles that pass the intersection per hour

The null hypothesis in a hypothesis test refers to __________.

the default state of nature/ status quo

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 5.00. A sample of 37 honors students is taken and is found to have a mean GPA equal to 5.10. The population standard deviation is assumed to equal 0.40. The parameter to be tested is __________.

the mean GPA of the university honors students

The basic principle of hypothesis testing is to assume that

the null hypothesis is true and see if the sample data contradict this assumption.

If the chosen significance level is α = 0.05, then __________.

there is a 5% probability of rejecting a true null hypothesis

We use sample information to make inferences regarding the parameter--------- population parameters of interest.

unknown

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 __________.

z = 1.50

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 760 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 710. Assume that the population standard deviation is 360. The value of the test statistic is __________.

z = −1.389

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 11 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement—students were not as late. Assume a population standard deviation for bus arrival time of 11 minutes. The value of the test statistic is __________.

z = −1.64

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the test statistic is __________.

z = −1.8545

When performing a hypothesis test on μ when σ is known, H0 can never be rejected if

z ≥ 0 for a left-tailed test.

A Type I error is commonly denoted as:

α (alpha)