ISDS Exam 3
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 __________. a) more concerned about type 1 error b) more concerned about type 2 error c) concerned about both type 1 and 2 errors d) not concerned at all
a
Steps of the p-value approach to hypothesis testing
1. specify the null and alternative hypothesis 2. specify the significance level 3. calculate the value of the test statistic and its p-value 4. state the conclusion and interpret results
a (alpha)
a type 1 error is denoted as
p
as a point estimate of the population proportion, we calculate
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 $16,700. A random sample of 27 students had an average debt load of $17,900. It is believed that the population standard deviation for student debt load is $4,020. The α is set to 0.05. The p-value for this hypothesis test would be __________. a) .157 b) .121 c) .060 d) .047
b
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 __________. a) z = −2.052 b) z = −1.8545 c) z = 1.8545 d) z = 2.052
b
Right tailed test
z < or equal to 0
True
for a given sample size, any attempt to reduce the likelihood of making one type of error will increase the likelihood of the other error
Alternative Hypothesis
in a hypothesis test, it contradicts the default state or status quo specified in the null hypothesis (HA)
Null Hypothesis
in a hypothesis test, it corresponds to a presumed default state of nature or status quo (HO)
P value
in a hypothesis test, probability of observing a sample result that is at least as extreme as the one derived from the given sample, under the assumption that the null hypothesis is true - most researchers and practitioners favor this
Type 2 Error
in a hypothesis test, this error occurs when the decision is to not reject the null hypothesis when the null hypothesis is false
Interpret
it is not sufficient to end the analysis with a conclusion that you reject the null hypothesis or you do not reject the null hypothesis. You must ______ the results
Significance level
the allowed probability of making a type 1 error
Left tailed test
z > or equal to 0
S
If population standard deviation is unknown, it can be estimated by using
reject
If sample evidence is inconsistent with the null hypothesis, we __________ the null hypothesis
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 a) the average number of automobiles that pass the intersection per hour b) the number of automobiles that pass the intersection per hour c) the proportion of automobiles that pass the intersection per hour d) the standard deviation of the number of automobiles that pass the intersection per hour
a
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 __________. a) reject H0; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 b) reject H0; we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 c) not reject H0; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 d) not reject H0; we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20
a
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? a) left tailed b) right tailed c) two tailed d) there is not enough information to answer
a
If the chosen significance level is α = 0.05, then __________. a) there is a 5% probability of rejecting a true null hypothesis b) there is a 5% probability of accepting a true null hypothesis c) there is a 5% probability of rejecting a false null hypothesis d) there is a 5% probability of accepting a false null hypothesis
a
two tailed
a test in which the null hypothesis can be rejected on either side of the hypothesized value of the population parameter
One tailed
a test in which the null hypothesis is rejected only on one side of the hypothesized value of the population parameter
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? a) t35 = 0.33 b) z = 0.33 c) t35 = 2.00 d) z = 2.00
c
A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 5 pCi/L. The school samples the air for 16 days and finds an average concentration of 5.4 pCi/L with a standard deviation of 1 pCi/L. The value of the test statistic is __________. a) t15 = -1.60 b) z = -1.60 c) t15 = 1.60 d) z = 1.60
c
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 __________. a) z = -1.50 b) t35 = -1.50 c) z = 1.50 d) t35 = 1.50
c
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? a) H0:μ=8,HA:μ≠8 b) H0:μ<12,HA:μ≥12 c) H0:μ≥12,HA:μ<12 d) H0:X≥8,HA:X<8
c
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 __________. a) H0:μ≤800,HA:μ>800 b) H0:X≤800,HA:X>800 c) H0:μ≥800,HA:μ<800 d) H0:X≥800,HA:X<800
c
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 5.40. A sample of 38 honors students is taken and is found to have a mean GPA equal to 5.50. The population standard deviation is assumed to equal 0.40. The parameter to be tested is __________. a) the proportion of honors students with a GPA exceeding 5.4 b) the mean GPA of all university students c) the mean GPA of 5.5 for the 38 selected honors students d) the mean GPA of the university honors students
d
An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 14 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 20 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 14.8 pounds with a standard deviation of 2.6 pounds. The test statistic for this hypothesis would be __________. a) -1.38 b) 1.70 c) -1.70 d) 1.38
d
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 __________. a) reject the null hypothesis and conclude that the population mean is significantly different from 0 b) reject the null hypothesis and conclude that the population mean is significantly different from 0 c) do not reject the null hypothesis and conclude that the population mean is significantly different from 0 d) do not reject the null hypothesis and conclude that the population mean is not significantly from 0
d
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, 14 minutes late. After the schedule adjustment, the first 25 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 14 minutes. The value of the test statistic is __________. a) t35 = -0.33 b) z = -0.33 c) t35 = -2.14 d) z = -2.14
d
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 750 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 700. Assume that the population standard deviation is 370. The value of the test statistic is __________. a) t99 = -1.351 b) t99 = 1.351 c) z = 1.351 d) z = -1.351
d
Type 1 Error
error is committed when we reject the null hypothesis when the null hypothesis is true
hypothesis testing
resolves conflicts between two competing opinions
Critical value
the __________ ____________ approach to hypothesis testing is attractive when a computer is unavailable and all calculations must be done by hand
Two
the hypothesis testing procedure enables us to make of ___________ decisions
Default state of nature
the null hypothesis in a hypothesis
a
the probability of committing a type 1 error: B = the probability of committing a type 2 error
