ISDS 2000 Exam 3 Review
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 or False
True
The decision rule is
- Reject Ho if the p-value < a or - Do not reject H0 if p-value ≥ a
An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 11 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 24 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 11.8 pounds with a standard deviation of 2.7 pounds. The test statistic for this hypothesis would be __________.
1.45
As a general guideline, we use the ____________ ____________ as a vehicle to establish something new-that is, contest the status quo.
alternative hypothesis
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
Test Statistic for μ when σ is known
z = x̄- μ0 / σ /√n
The significance level of a hypothesis is defined as ______?
100a%
Two-tailed test
we can reject the null hypothesis on either side of the hypothesized population parameter. Ex: H0: μ = μ0 vs Ha: μ ≠ μ0
What are the 3 steps when formulating the competing hypotheses?
1. Identify the relevant population parameter of interest. 2. Determine whether it is a one- or two-tailed test. 3. Include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim.
4 Step Procedure Using the p-Value Approach
1. Specify the null and alternative hypothesis. 2. Specify the significance level. 3. Calculate the value of the test statistic and the p-value. 4. State the conclusion and interpret results.
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 900 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 850. Assume that the population standard deviation is 410. The value of the test statistic is __________.
z = -1.220
Test Statistic for μ when σ is unknown
tdf = x̄- μ0 s /√n
Significance level
the allowed probability of making a Type I error
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 p-value is also referred to as the __________ _________ of a Type I error.
observed probability
A hypothesis test can be ________ or __________.
one-tailed or two-tailed
If sample evidence is NOT inconsistent with the null hypothesis, we
do NOT reject the null hypothesis
Type I Error
this error occurs when the decision is to reject the null hypothesis when the null hypothesis is true
If Ha: μ < μ0
Left-tailed probability: P(Z ≤ z)
It is not correct to conclude that
"we accept the null hypothesis"
What are the two approaches to implementing a hypothesis test?
1. p-value 2. critical value approach
If sample evidence is inconsistent with the null hypothesis, we...
reject the null hypothesis
The null hypothesis in a hypothesis test refers to __________.
the default state of nature
Test Statistic for p
z= (p-po) / √(po(1-po)/n)
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 $17,100. A random sample of 31 students had an average debt load of $18,300. It is believed that the population standard deviation for student debt load is $4,090. The α is set to 0.05. The p-value for this hypothesis test would be __________.
0.103
The null hypothesis is specified with which one of the following signs
= , ≤ , ≥
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<800
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<12
Alternative Hypothesis (Ha)
contradicts the default state or status quo specified in the null hypothesis
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
Null Hypothesis (H0)
corresponds to a presumed default state of nature or status quo
If Ha: μ > μ0
Right-tail probability: P(Z ≥ z)
Which approach is attractive when a computer is unavailable and all calculations must be done by hand?
critical value approach
If Ha: μ ≠ μ0
Two-tail probability: 2P(Z ≥ z) if z > 0 or 2P(Z ≤ z) if z<0
A(n) __________ error is committed when we reject the null hypothesis when the null hypothesis is true.
Type I
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
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
Degrees of Freedom (df) =
n - 1
The parameter p represents the
proportion of observation with a particular attribute
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
We use the hypothesis testing framework to
resolve conflicts between two competing hypotheses on a particular population parameter of interest
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 16 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 __________.
t15 = 1.60
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
p-value
the likelihood of obtaining a sample mean that is at least as extreme as the one derived from the given sample
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 5.10. A sample of 33 honors students is taken and is found to have a mean GPA equal to 5.20. The population standard deviation is assumed to equal 0.40. The parameter to be tested is __________.
the mean GPA of the university honors students
If the chosen significance level is α = 0.05, then __________.
there is a 5% probability of rejecting a true null hypothesis
Type II Error
this error occurs when the decision is to not reject the null hypothesis when the null hypothesis is false
One-tailed test
we can reject the null hypothesis only on one side of the hypothesized value of the population parameter. Ex: H0: μ ≥ μ0 vs Ha: μ < μ0
We conduct a hypothesis test to determine
whether or not sample evidence contradicts the null hypothesis
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
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, 20 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 20 minutes. The value of the test statistic is __________.
z = −3.60
The alternative hypothesis is specified with which of the corresponding opposite signs
≠ , <, >