ISDS Robert Woosley
If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α = 0.05, then the correct conclusion is to
not reject the null hypothesis
A Type I error occurs when we
reject the null hypothesis when it is actually true
When conducting a hypothesis test concerning the population proportion, the value of the test statistic is calculated as
z= pbar-p0 ------------- Square root of p0(1-p0)/n
What type of hypothesis test should we use to test whether borrowers from this particular bank who receive HAMP modifications are more likely to re-default than those who receive non-HAMP modifications?
A hypothesis test for p1 - p2.
Which of the following are two-tailed tests?
H0: μ = 10, HA: μ ≠ 10
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
The null hypothesis in a hypothesis test refers to
the default state of nature
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= xbar-mean -------------- SD/square root of sample
You want to test whether the population variance differs from 50. From a sample of 25 observations drawn from a normally distributed population, you calculate s2 = 80. When conducting this test at the 5% significance level, the, critical value is
14.400
When testing the difference between two population means and the population variances are unknown and unequal, the degrees of freedom is calculated as 34.7. What degrees of freedom should be used to find the p-value of the test?
34
Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916 Assume that profits are normally distributed. Which of the following is the correct value of the test statistic?
7.375
What type of data is required to compare prices of the same textbooks sold by two different vendors? A) Dependent random samples with qualitative data. B) Dependent random samples with quantitative data. C) Independent random samples with qualitative data. D) Independent random samples with quantitative data.
B
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. Identify the correct null and alternative hypotheses to test the politician's claim.
H0: p ≤ 0.50 and HA: p > 0.50
A tutor promises to improve GMAT scores of students by more than 50 points after three lessons. To see if this is true, the tutor takes a sample of 49 students' test scores after and before they received tutoring. The mean difference was 53 points better after tutoring, with a standard deviation of the difference equal to 12 points. Let µD denote the mean of the difference: score after tutoring minus score before tutoring. Which of the following hypotheses will determine if the students improved their test scores by more than 50 points after being tutored? Which of the following is the correct value of the test statistic? Assuming α = 0.05, which of the following is the appropriate critical value?
H0: µD ≤ 50, HA: µD > 50 t48 = 1.7500 t0.05,48 = 1.677
What is the decision rule when using the p-value approach to hypothesis testing?
Reject H0 if the p-value < α.
The following are the competing hypotheses and the relevant summary statistics Η0: a1^2/a2^2≤ 1, ΗA: a1^2/ a2^2> 1. S1^2= 415 S2^2= 323 n1 = 10 n2 = 9 Which of the following statements is correct, regarding the assumptions for conducting the hypothesis test?
The samples are independent and drawn from normally distributed populations.
Packaged candies have three different types of colors. Suppose you want to determine if the population proportion of each color is the same. The most appropriate test is the
goodness-of-fit test for a multinomial experiment
Which of the following is the value of x for which P(F(6,10)>x)= 0.025? -
4.07
Find Xa/2df^2 and X1-a/2df^2 under the following scenarios. a. A 90% confidence level with n = 10. b. A 95% confidence level with n = 15. c. A 99% confidence level with n = 20.
a. 16.919 and 3.325 b. 26.119 and 5.629 c. 38.582 and 6.844
The ________ is the probability distribution of the sum of several independent squared standard normal random variables.
Xdf^2 distribution
Consider the following hypotheses that relate to the medical field: H0: A person is free of disease. HA: A person has disease.
a false positive
Find the value x for which a. P(x17^2≥ x) = 0.10. b. P(x17^2 < x) = 0.10. c. P( x23^2≥ x) = 0.05. d. P( x23^2< x) = 0.05.
a. 24.769 b. 10.085 c. 35.172 d. 13.091
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
If P(x6^2 ≥ x) = 0.05, then the value of x is
12.592
A card-dealing machine deals spades (1), hearts (2), clubs (3), and diamonds (4) at random as if from an infinite deck. In a randomness check, 1,600 cards were dealt and counted. The results are shown below. Spades- 410 Hearts- 405 Clubs- 370 Diamonds- 415 For the goodness-of-fit test, the degrees of freedom are
3
The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared. He would like to add an additional billing counter if the variance exceeds the cut-off. He checks the recent sample data. For a random sample of 24 customer waiting times, he arrives at a sample variance of 3.8 minutes-squared. The manager assumes the waiting times to be normally distributed. At α = 0.05, which of the following is the critical value
35.172
The student senate at a local university is about to hold elections. A representative from the women's sports program and a representative from the men's sports program must both be elected. Two candidates, an incumbent and a challenger, are vying for each position. A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates. In a sample of 100 voters, 67 said that they would vote for the women's incumbent candidate. In a separate sample of 100 voters, 55 said they would vote for the men's incumbent candidate. Let p1 and p2 be the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs, respectively. Which of the following hypothesis tests must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates? Which of the following are the competing hypotheses to determine whether the percentages of supporting votes are different between the two incumbent candidates? Use a 5% level of significance. Which of the following is(are) critical value(s) of the appropriate test?
A z test of two population proportions with a zero hypothesized difference. H0: p1 = p2, HA: p1 ≠ p2 -1.960 and ±1.960
Suppose you want to determine if gender and major are independent. Which of the following tests should you use?
Chi-square test for independence
A financial analyst maintains that the risk, measured by the variance, of investing in emerging markets is more than 280(%)2. Data on 20 stocks from emerging markets revealed the following sample results: = 12.1% and s2 = 361(%)2. Assume that the returns are normally distributed. Which of the following is the correct conclusion of the financial analyst's claim?
Do not reject H0. The financial analyst's claim is not supported by the sample data at 1% significance level
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 H0: μ = 0, HA: μ ≠ 0?
Do not reject H0; we cannot conclude that the mean differs from zero.
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. In testing the university's belief, the appropriate hypotheses are
H0: p ≥ 0.20, HA: p < 0.20
Define the null and alternative hypotheses to test whether borrowers who receive HAMP modifications default less than borrowers who receive non-HAMP modifications. Let p1 and p2 represent the proportion of borrowers who received HAMP and non-HAMP modifications that did not re-default, respectively.
H0: p1 - p2 ≥ 0, HA: p1 - p2 < 0
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. A random sample of 25 weeks is collected for Tuesday a different sample of 25 weeks is collected for Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Let μ1 be the population mean of Tuesday, μ2 be the population mean of Wednesday, and μD be the mean difference for a matched-pairs sampling. What are the appropriate hypotheses to determine whether there is a difference, on average, in attendance between shows on Tuesday evening and Wednesday evening? Which of the following is the value of the appropriate test statistic?
H0: µ1 - µ2 = 0, HA: µ1 - µ2 ≠ 0 -2.4736
In August 2010, Massachusetts enacted a 150-day right-to-cure period that mandates that lenders give homeowners who fall behind on their mortgage an extra five months to become current before beginning foreclosure proceedings. Policymakers claimed that the policy would result in a higher proportion of delinquent borrowers becoming current on their mortgages. To test this claim, researchers took a sample of 244 homeowners in danger of foreclosure in the time period surrounding the enactment of this law. Of the 100 who fell behind just before the law was enacted, 30 were able to avoid foreclosure, and of 144 who fell behind just after the law was enacted, 48 were able to avoid foreclosure. Let p1 and p2 represent the proportion of delinquent borrowers who avoid foreclosure just before and just after the right-to-cure law is enacted, respectively. Which of the following is the correct competing hypotheses that will test the policymakers' claim? Which of the following is the appropriate test statistic value to analyze the claim at the 10% significance level? Which of the following is the appropriate p-value to verify the claim? Assuming α = 0.10, does the evidence support the policymakers' claim?
H0:p1-p2 ≥ 0,HA:p1-p2 < 0 z = −0.549 p=0.2915 No, because the p-value is greater than the significance level.
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. In testing the university's belief, how does one define the population parameter of interest?
It's the proportion of honors graduates with a GPA of 3.00 or below.
When conducting a hypothesis test, which of the following decisions represents an error?
Rejecting the null hypothesis when it is true.
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?
The mean score on the eighth-grade reading comprehension test
For a multinomial experiment, which of the following is not true?
The trials are dependent
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 $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The confidence interval for this hypothesis test would be
[$16,788.22, $19,611.78]
A random sample of 18 observations is taken from a normal population. The sample mean and sample standard deviation are 76.4 and 4.2, respectively. What is an 80% interval estimate of the population variance?
[12.107, 29.735]
Which of the following is a 98% confidence interval for the population variance when the sample variance is 20 for a sample of 10 items from a normal population?
[8.308, 86.207]
Which of the following pairs of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using independent random sampling?
c) H0: µ1 - µ2 ≥ 0, HA: µ1 - µ2 < 0
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 schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the decision is to
reject H0; we can conclude that the mean concentration of radon gas is greater than the safe level
Assume the competing hypotheses take the following form: H0: µ1 - µ2 = 0, HA: µ1 - µ2 ≠ 0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also assume that the populations are normally distributed and we use independent sampling. The population variances are not known and assumed to be unequal. Which of the following expressions is the appropriate test statistic?
tdf = xbar1-xbar2 ------------- Square root of s1^2/n1+s2^2/n2
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