BNAD 276 conceptual chapter 9
a statistical 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 of his 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 he accuses a student of cheating and he is actually incorrect. Consider the null hypothesis, "the student is not cheating". what is the probability of a Type 1 error
1%
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, the critical value(s) are?
1.645
which of the following answers represent the objective of a hypothesis test
Both b and 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. The value of the test statistic
H
Many cities around the United States are installing LED streetlights, in part to combat crime by improving the visibility after dusk. an urban police department claims that the proportion of crimes committed after dusk will fall below the current level of .84 if LED streetlights are installed. Specify the null and alternative hypothesis to test the polices departments claim
Ho: P≥.84 and Ha:p<.84
which of the following are two-tailed tests
Ho: U=10 versus Ha: u≠10
t is generally believed that no more than 0.50 of all babies in a town in texas are born out of wedlock. a political claims that the proportion of babies that are born out of wedlock is increasing. Identify the correct null and alternative hypothesis to test the politicians claim
Ho: p≤.50 and Ha: p>.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 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. In order to determine whether there has been a decrease in the average number of customers visiting the dealership daily ,the appropriate hypotheses are?
Ho: u ≥ 800, and Ha: u<800
which of the following represents an appropriate set of hypotheses?
Ho: u=0, Ha: u ≠ 0
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. In order to establish whether the mean GPA exceeds 3.50, the appropriate hypothesis are?
Ho: u≤3.50 and Ha: u>3.50
True or False: The hypothesis typically corresponds to a presumed default state of nature
True
true or false: a hypothesis test regarding the population mean (U) is based on the sampling distribution of the sample mean (X with bar over)
True
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 II error is often referred to as
a false negative
consider the following hypothesis that relate to the medical field: Ho:A person is free of disease. Ha: A person has a disease. In this instance, a type I error is often referred to as
a false positive
when conducting a hypothesis test for a given sample size if a is increased from 0.05 to .10 then
all of the above are correct
which of the following are one-tailed tests?
both A and C
the alternative hypothesis typically
contests the status quo for which a corrective action may be required
for a given sample size, n
decreasing the probability of a type 1 error A, will increase the probability of a type II error B
consider the following competing hypothesis: Ho:u=0 and Ha: u≠0. the value of the test statistic is z=-1.38. if we chose a 5% significance level, then we_
do not reject the null hypothesis and conclude that the population ean is not significantly different from zero
A type II error occurs when we
do not reject the null when it is actually false
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, the decision is to?
do not reject the null, we cannot conclude that the mean GPA is significantly greater than 3.50
True or false: a type II error is made when we reject the null hypothesis and the null hypothesis is actually false
false
True or false: on the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis"
false
True or false: the alternative hypothesis typically agrees with the status quo
false
True or false: the critical value approach specifies a range of values, also called the rejection region, such that if the value of the test statistic falls into this range, we do not reject the null hypothesis
false
in general, the null and alternative hypotheses are
mutually exclusive
when we reject the null hypothesis when it is actually false we have committed
no error
if the p-value for a hypothesis test is 0.07 and the chosen level of significance is a=.05, then the correct conclusion is to
not reject the null hypothesis
a one-tailed hypothesis test of the population mean has
only one critical value
when conducing a hypothesis test for a given sample size, if the probability of a type I error decreases, then the
probability of incorrectly accepting the null increases
what is the decision rule when using the p-value approach to hypothesis testing?
reject Ho if the p-value < alpha
if the p-value for the hypothesis test is 0.027 and the chosen level of significance is a=0.05, the the correct conclusion is to
reject the null hypothesis
A type I error occurs when we
reject the null when it is actually true
when conducting a hypothesis test, which of the following decisions represents an error
rejecting the null hypothesis when it is true
which of the following types of test may be preformed?
right-tailed, left-tailed, and two-tailed test
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. the advisor tests the following hypotheses: H0: u≤300 versus Ha:u>300, u stands for
the average number of automatsbles that pass the intersection per hour
it is generally believed that no more than 0.50 of all babies in a town in texas are born out of wedlock. a political claims that the proportion of babies that are born out of wedlock is increasing. When testing the two hypotheses, H0: p ≤ .50 and Ha: p>0.50, p stands for
the current proportion of babies born out of wedlock
it is generally believed that no more than 0.50 of all babies in a town in texas are born out of wedlock. a political claims that the proportion of babies that are born out of wedlock is increasing. in testing, the politicians claim, how does one define the population parameter of interest?
the current proportion of babies born out of wedlock
the null hypothesis in a hypothesis in a hypothesis test refers to
the default state of nature
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. the advisor tests the following hypotheses: H0: u≤300 Ha:u>300 The consequences of committing type I error would be that___
the franchiser builds on an unacceptable site
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. the advisor tests the following hypotheses: H0: u≤300 Ha:u>300 The consequences of committing type II error would be that___
the franchiser does not build on an acceptable site
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?
the mean GPA of the 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 hypothesis , Ho; u ≥ 6 and Ha:u < 6, u stands for
the mean delivery time
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 population parameter to be tested is?
the mean number of customers visiting the dealership per day
the national average for an 8th grade rating comprehension test is .73. a school district claims that its eighth- graders outperform the national average. in testing the school districts claim, how does one define the population parameter of interest?
the mean score on the 8th grade reading comprehension test
if the null hypothesis is rejected at 1% significance level, then
the null hypothesis will be rejected at 5% significance level
a hypothesis test regarding the population mean is based on
the sampling distribution of the sample mean
If the chosen significance level is a=0.05, then
there is a 5% probability of rejecting a true null hypothesis
True or false: 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
True or false: under the assumption that the null hypothesis is true as a quality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from a given sample.
true
true or false: a type 1 error is committed when we reject the null hypothesis which is actually true
true
true or false: 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
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
a two-tailed hypothesis test of the population mean or population proportion has
two critical values, one positive and one negative
A professional sports organization is going to implement a test for steroids. the test gives a positive reaction to 94% of the people who have taken the steroid. However, it is erroneously gives a positive reaction in 4% of the people who have not taken the steroid. what is the probability of a type I and type II error using the null hypothesis "the individual has not taken the steroids"
type I: 4% and Type II 6%
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
