Unit 3 Test STA 2023 McGraw Hill
When comparing two population means, their hypothesized difference _________ .
may assume any value We are interested in testing for any difference between the population means.
When we reject the null hypothesis when it is actually false, we have committed _________.
no error
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. Two independent samples of 25 weeks are collected for Tuesday and 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. Which of the following is the value of the appropriate test statistic?
z = -2.4736
On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What is the probability that two light bulbs will be defective?
0.0746
The probability P(Z > 1.28) is closest to _______.
0.10
The probability P(Z < -1.28) is closest to _______.
0.10 Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z.
Consider the following discrete probability distribution. x -10 0 10 20 P(X = x) 0.35 0.10 0.15 0.40 What is the probability that X is greater than 0?
0.55
The values of the formula4.mml distribution range from negative infinity to infinity
False
A financial analyst examines the performance of two mutual funds and claims that the variances of the annual returns for the bond funds differ. To support his claim, he collects data on the annual returns (in percent) for the years 2001 through 2010. The analyst assumes that the annual returns for the two emerging market bond funds are normally distributed. Use the following summary statistics. Mutual Fund 1 Mutual Fund 2 formula519.mml = 500 formula520.mml = 100 n1 = 10 n2 = 10 For the competing hypotheses formula521.mml which of the following is the correct approximation of the p-value?
0.02 and 0.05
The probability P(Z < -1.28) is closest to _______.
0.10
The null hypothesis typically corresponds to a presumed default state of nature.
True
The values taken from a normally distributed population are 21 23 25 27 28 35 30 32 33. Which of the following is a 95% confidence interval for the population variance.
[10.12, 81.43]
Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error. If there is no rough estimate formula259.mml of the population proportion, what value should be assumed for formula259.mml?
0.50
A politician wants to estimate the percentage of people who like his new slogan. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.08 for a 95% confidence interval?
151 For a desired margin of error E, the minimum sample size n required to estimate a formula276.mml confidence interval for the population proportion is computed as formula277.mml is a reasonable estimate of formula278.mml in the planning stage. Use z table.
The values of the formula4.mml distribution range from negative infinity to infinity.
False The values of the formula10.mml distribution range from zero to infinity.
Two random samples are considered independent if the observations in the first sample are different from the observations of the second sample.
False Two random samples are considered independent if the process that generates one sample is completely separate from the process that generates the other sample.
A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season. The first variety is milk chocolate while the second is milk chocolate filled with mint. It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances. Two independent samples of 18 observations each are collected for the holiday period. A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2.5 million. A sample mean of 13.5 million truffles filled with mint sold with a sample standard deviation of 2.3 million. Use milk chocolate as population 1 and mint chocolate as population 2. Which of the following are the appropriate hypotheses to determine if the average sales of the two varieties of truffles differ significantly during the holiday season?
H0: µ1 - µ2 = 0, HA: µ1 - µ2 ≠ 0 For independent sampling the two-tailed hypothesis test is H0: µ1 − µ2 = d0, HA: µ1 − µ2 ≠ d0.
Suppose Apple would like to test the hypothesis that the standard deviation for the web-browsing battery life of the iPad equals 3.0 hours. The following data represents the battery life, in hours, experienced by a random sample of six users: 10 14 12 16 10 6. Which of the following would be the correct hypothesis test?
H0:σ2 = 9.0, HA:σ2 ≠ 9.0 The competing hypotheses for the right-tailed test for the population variance are formula574.mml
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. In 2009, 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. When testing whether the dropout rate has decreased, the appropriate hypotheses are _____________
Ho: p greater than or equal to 0.081, Ha: p <0.081 The competing hypotheses are Ho: p ≥ po,HA: < po. It is referred to as a left-tailed test of the population proportion.
Edmunds.com would like to test the hypothesis that the standard deviation for the age of an imported car on the road is greater than the standard deviation for the age of a domestic car. The following data shows the ages of a random sample of import and domestic cars. Import 1 3 4 5 4 5 10 Domestic 4 5 4 6 5 4 6 Which of the following would be the correct hypothesis test?
Ho:sigma2/1 / sigma2/2 less than or equal to 1, Ha: sigma2/1 / sigma 2/2>1
How do the tdf and z distributions differ?
The tdf distribution has broader tails (it is flatter around zero). The tdf distribution has broader tails than the z distribution.
The required sample size for the interval estimation of the population mean can be computed if we specify the population standard deviation σ, the value of formula24.mml based on the confidence level formula25.mml, and the desired margin of error D. True
True
If a random sample of size n is taken from a normal population with a finite variance, then the statisticformula20.mmlfollows the tdf distribution with (n −1) degrees of freedom, df.
True If a random sample of size n is taken from a normal population with a finite variance, then the statisticformula21.mmlfollows the tdf distribution with (n −1) degrees of freedom, df.
The tdf distribution has broader tails than the z distribution.
True The tdf distribution has slightly broader tails than the z distribution.
Consider the following sample regression equation formula185.mml = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to ______________
decrease by 60,000
Consider the following sample regression equation formula185.mml = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to ______________
decrease by 60,000 In the simple linear regression model the coefficient b1 measures the change in the predicted value of the response variable formula184.mmlgiven a unit increases in the associated explanatory variable. Estimate the change.
The result of placing a larger sample variance in the numerator of the formula402.mml test statistic allows us to
focus only on the right tail of the distribution.
What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E = 1.5? The population standard deviation is known to be 10.75.
n=198
A statistics professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes independently random samples, each of size 36, consisting of students who took a morning and an afternoon class, and compares the scores of each group on a common final exam. He finds that the morning group scored an average of 74 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but is assumed to be equal for morning and evening classes. Let µ1 and µ2 represent the population mean final exam scores of statistics' courses offered in the morning and the afternoon, respectively. Compute the appropriate test statistic to analyze the claim at the 1% significance level.
t70=2.811
A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, Ho:μ ≥ 6 and HA:μ < 6, μ stand for _____________.
the mean delivery time Hypothesis testing is used to resolve conflicts between two competing hypotheses on a particular population parameter of interest.
Consider the following sample regression equation formula191.mml= 200 + 10x, where y is the supply for Product A (in 1000s)(in 1,000s) and x is the price of Product A (in $). The slope coefficient indicates that if ___________.
the price of Product A increases by $1, then on average, supply increases by 10,000
Which of the following set of hypotheses is used to test if the mean of the first population is smaller than the mean of the second population, using matched-paired sampling?
H0: µD ≥ 0, HA: µD < 0 In general, we want to test whether the mean difference µD is equal to, greater than, or less than a given hypothesized mean difference d0.
The values taken from a normally distributed population are 21 23 25 27 28 35 30 32 33. Which of the following is a 95% confidence interval for the population variance.
[10.12, 81.43] A 100(1 − α)% confidence interval of the population variance σ2 is computed as formula237.mml.A point estimate of the population variance is computed as formula238.mml.
We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?
[11.7019, 13.2981] The confidence interval for the population mean is computed as formula69.mml. Use z table.
Peter applied to an accounting firm and a consulting firm. He knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. Assume that receiving an offer from one firm is independent of receiving an offer from the other. What is the probability that both firms offer Peter a job?
0.06
An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes's theorem, the posterior probability that the company will experience a decline is 18%.
69%
What is the decision rule when using the p-value approach to hypothesis testing?
Reject Ho if the p-value < α.
A two-tailed test is used to determine if two population variances differ. The null hypothesis takes the form H0
sigma2/1 / sigma2/2 =1 The competing hypotheses for the two-tailed test for the ratio of two population variances are formula470.mmlformula471.mml, formula472.mmlformula473.mml.
When testing the difference between two population means under independent sampling, we use the z distribution if _________ .
the population variances are known If the population variances are known, use z distribution; if they are unknown, use - tdf distribution.
A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.
False A confidence interval provides a range of values that, with a certain level of confidence, contains the population parameter of interest.
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(are) the appropriate critical value(s) to test the new coach's claim at the 1% significance level?
2.438 For a right-tailed test with α = 0.05 and df = n - 1, the critical value is tα,df and is defined using t table.
How does the width of the interval respond to the changes in the confidence interval?
The width of the interval increases with an increase in the confidence interval. The width of the interval increases with an increase in the confidence level.
The required sample size for the interval estimation of the population mean can be computed if we specify the population standard deviation σ, the value of formula24.mml based on the confidence level formula25.mml, and the desired margin of error D.
True
The value of the test statistic for the hypothesis test of the population variance, σ2 is computed as formula19.mml=formula20.mml.
True
The value of the test statistic to test the ratio of two population variances is S2/1 /S2/2
True
The _____ is the probability distribution of the sum of several independent squared standard normal random variables.
X2dF distribution In general, the formula210.mml distribution is the probability distribution of the sum of several independent squared standard normal random variables.
A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy". Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy."
0.2116,0.2484
On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis."
False On the basis of sample information, we either "reject the null hypothesis" or "do not reject the null hypothesis." Only one of two hypotheses is true and the hypotheses cover all possible values of the population parameter.
Statistical inferences pertaining to σ2 are based on which of the following distributions?
The chi-square distribution Statistical inferences regarding to σ2 are based on formula222.mml or chi-square distribution.
The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198. Which of the following is the approximate value of the assumed estimate of the population standard deviation?
10.7688 For a desired margin of error E, the minimum sample size n required to estimate a 1formula226.mml confidence interval for the population mean is computed as 1formula227.mml 1formula228.mml is a reasonable estimate of 1formula229.mml in the planning stage. Because the required sample size is rounded up the following is correct: 1formula230.mml . It can be derived that 1formula231.mml Use z table.
On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis." True
False On the basis of sample information, we either "reject the null hypothesis" or "do not reject the null hypothesis." Only one of two hypotheses is true and the hypotheses cover all possible values of the population parameter.
The confidence interval for the difference formula34.mml is based on the same approach used in the case of one sample: Point Estimate ± Standard Error
False The confidence interval for the difference in population means is based on the same approach used in the case of one sample: Point Estimate ± Margin of Error.
The difference between the two sample means formula9.mml is an interval estimator of the difference between two population means formula10.mml.
False The difference between the two sample means formula11.mml is a point estimator of the difference between two population means formula12.mml.
The parameter of interest for inferences regarding the ratio of two population variances is their sum formula39.mml.
False The parameter of interest for inferences regarding the ratio of two population variances as the ratio of the population variances formula40.mml.
The t distribution table lists tdf values for selected lower-tail probabilities and degrees of freedom df.
False The t distribution table lists tdf values for selected upper-tail probabilities and degrees of freedom df.
The tdf distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the tdf distribution is similar to the z distribution.
False The tdf distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. As df increases, the tdf distribution becomes more similar to the z distribution; it is identical to the z distribution when df is infinity.
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 is the correct value of the test statistic?
t48 = 1.7500 Testing the mean differences in matching-pairs sampling, a right-tailed test should be performed: H0: µD ≤ d0, HA: µD > d0. The test statistic is computed as formula301.mml
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: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________.
the franchiser builds on an unacceptable site A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true.
The probability P(Z > 1.28) is closest to _______.
0.10 Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. Compute P(Z > z) = 1 - P(Z ≤ z)
The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. Chocolate Vanilla Swirl Under 25 years old 40 20 15 At least 25 years old 15 40 20 What is the probability that a randomly selected customer prefers vanilla?
0.40
Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error. If there is no rough estimate formula259.mml of the population proportion, what value should be assumed for formula259.mml
0.50
Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error. If there is no rough estimate formula259.mml of the population proportion, what value should be assumed for formula259.mml?
0.50 For a desired margin of error E, the minimum sample size n required to estimate a formula256.mml confidence interval for the population proportion is computed as formula257.mml is a reasonable estimate of formula258.mml in the planning stage. Use z table.
Chauncey Billups, a current shooting guard for the Los Angeles Clippers, has a career free-throw percentage of 89.4%. Suppose he shoots six free throws in tonight's game. What is the probability that Billups makes all six free throws?
0.5105
Which of the following is the value of x for which formula299.mml
18.307 For a formula295.mml distributed random variable, we use the notation formula296.mml to represent such that the area in the right tail of a distribution is formula297.mml. Or Pformula298.mml=formula297.mml. Use X2 distribution table to find formula296.mml with df and formula297.mml given.
The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.
2.92 + 2.093 (0.16/sqrt(20)) Because the population standard deviation is unknown use tdf distribution. The confidence interval of the population mean is computed as formula100.mml. Use t table.
A university wants to compare out-of-state applicants' mean SAT math scores (μ1) to in-state applicants' mean SAT math scores (μ2). The university looks at 35 in-state applicants and 35 out-of-state applicants. The mean SAT math score for in-state applicants was 540, with a standard deviation of 20. The mean SAT math score for out-of-state applicants was 555, with a standard deviation of 25. It is reasonable to assume the corresponding population standard deviations are equal. To calculate the confidence interval for the difference μ1 - μ2, what is the number of degrees of freedom of the appropriate probability distribution?
68 When the population variances are unknown but assumed equal, the interval estimation of μ1 - μ2 requires the use of the tdf distribution with df = n1 + n2 - 2.
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 The test statistic for the hypothesis test of the population variance σ2 is computed as formula317.mml. A point estimate of the population variance is computed as formula318.mml.
Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers' tastes and current fads. Consider the following growth rates (in percent) for two companies in this industry, Hasbro and Mattel. Year Hasbro Mattel 2005 3.0 1.5 2006 2.1 9.1 2007 21.8 5.7 2008 4.8 -0.1 2009 1.2 -8.2 Which of the following is(are) the critical value(s) at α = 0.05?
9.60 and 0.10 The competing hypotheses for the two-tailed test for the population variance are formula592.mml It is a two-tailed test.The critical values for a two-tailed test formula593.mml and formula594.mml can be found using F distribution table given α,df1, and df2.
Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?
A larger sample size reduces the margin of error. If we are able to increase the size of the sample, the larger nreduces the margin of error for the interval estimates.
What type of test for population means should be performed when examining a situation in which employees are first tested, then trained, and finally retested?
A t test under dependent sampling. A common case of dependent sampling is referred to as matched-pairs sampling and tdf distribution should be used for test statistic.
Which of the following are one-tailed tests?
Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400 A two-tailed test is defined when the alternative hypothesis includes the sign "≠". A one-tailed test involves a null hypothesis that can be rejected only on one side of hypothesized value.
Which of the following Excel's functions is used to obtain the right-tailed value for the formula402.mml statistic given any probability?
F.INV.RT(Probability, Deg_freedom1, Deg_freedom2) The Excel's function used to obtain the right-tailed formula402.mml value for any probability is F.INV.RT(Probability, Deg_freedom1, Deg_freedom2).
If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of formula28.mml is approximately normal only if the sum of the sample observations is sufficiently large—that is, when formula29.mml
False If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of formula30.mml is approximately normal only if both sample sizes are sufficiently large-that is, when formula31.mml and formula32.mml
For a given confidence levelformula5.mmland sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.
False For a given confidence levelformula6.mmland sample size n, the width of the confidence interval for the population mean is wider, the greater the population standard deviation σ.
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. Two independent samples of 25 weeks are collected for Tuesday and 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. What are the appropriate hypotheses to determine whether there is a difference in attendance for shows on Tuesday evening and Wednesday evening? Use Tuesday attendance as population 1 mean μ1 and Wednesday attendance as population 2 mean μ2, or μD as the mean difference in matched-pairs sampling.
H0: µ1 - µ2 = 0, HA: µ1 - µ2 ≠ 0 To recognize a matched-pairs experiment, we watch for a natural pairing between one observation in the first sample and one observation in the second sample. If a natural pairing exists, the experiment involves matched samples. The competing hypotheses are H0: µ1 - µ2 = d0, HA: µ1 - µ2 ≠ d0
A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µ1 and µ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Specify the competing hypotheses to determine if fertilizer A contains more nitrogen per batch than fertilizer B
H0: µ1 - µ2 ≤ 0, HA: µ1 - µ2 > 0 If we need to test if the mean of the first population is greater than the mean of the second population, we should use the right-tailed test, which is H0: µ1 −µ2 ≤ d0, HA: µ1 −µ2 > d0.
A statistics professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes independently random samples, each of size 36, consisting of students who took a morning and an afternoon class, and compares the scores of each group on a common final exam. He finds that the morning group scored an average of 74 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but is assumed to be equal for morning and evening classes. Let µ1 and µ2 represent the population mean final exam scores of statistics' courses offered in the morning and the afternoon, respectively. Which of the following hypotheses will test the professor's claim?
H0: µ1 - µ2 ≤ 0, HA: µ1 - µ2 > 0 In testing µ1 − µ2 when population variances are unknown but assumed to be equal, a right-tailed test for the difference between two population means should be performed: H0: µ1 - µ2 ≤ d0, HA: µ1 - µ2 > d0, if we are looking for the difference to be positive.
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?
H0: µD ≤ 50, HA: µD > 50 Testing the mean differences in matching-pairs sampling, a right-tailed test should be performed: H0: µD ≤ d0, HA: µD > d0.
Which of the following set of hypotheses is used to test if the mean of the first population is smaller than the mean of the second population, using matched-paired sampling?
H0: µD ≥ 0, HA: µD < 0
Which of the following represents an appropriate set of hypotheses?
Ho:u=0 , Ha cannot equal 0 A parameter is always tested, the null and alternative hypotheses must be mutually exclusive and collectively exhaustive, and the equal sign must appear in the null hypothesis.
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. The parameter to be tested is the population proportion of honors graduates.
Which of the following is the necessary condition for creating confidence intervals for the population mean?
Normality of the estimator For the confidence interval, the estimator formula55.mml must be at least approximately normally distributed. By the central limit theorem, even when the population is not normally distributed, this condition is satisfied as long as the sample size 1formula56.mml
Which of the following is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling.
Only if n1 p1 less than or equal to 5 formula233.mml formula234.mml, and formula235.mml Statistical inference regarding two population proportions is valid only if formula224.mml formula225.mmland 2formula226.mml where 2formula227.mml and 2formula228.mml are evaluated at formula229.mml and formula230.mml respectively.
What is the most typical form of a calculated confidence interval?
Point estimate ± Margin of error It is common to construct a confidence interval as Point estimate ± Margin of error.
What type of data would necessitate using a hypothesis test of the population proportion rather than a test of the population mean?
Qualitative The population proportion p is the essential descriptive measure when the data type is qualitative.
Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two peak hours, morning 8a.m. to 10 a.m. and evening 7p.m. to 9p.m., for the analysis. Assume that wait times are normally distributed. Wait Time (in seconds) Morning hours 8a.m.-10a.m. 97 101 115 107 129 98 96 132 118 104 123 128 95 127 112 Evening hours 7p.m.-9p.m. 95 92 89 90 102 96 85 81 84 100 97 80 98 79 99 At the 10% significance level, which of the following is the correct conclusion?
Reject H0. We conclude that the variance of wait time during morning peak hours differs from that during the evening peak hours
What is the decision rule when using the p-value approach to hypothesis testing?
Reject Ho if the p-value < α. The decision rule is to reject the null hypothesis if the p-value < α and not reject the null hypothesis if the p-value ≥ α.
Which of the following answers represents the objective of a hypothesis test?
Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true. Two correct decisions are possible: not rejecting the null hypothesis when the null hypothesis is true and rejecting the null hypothesis when the null hypothesis is false. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true includes both types of correct decisions.
When conducting a hypothesis test, which of the following decisions represents an error?
Rejecting the null hypothesis when it is true. A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true. A Type II error is made when we do not reject the null hypothesis and the null hypothesis and the null hypothesis is actually false.
When the required sample size calculated by using a formula is not a whole number, what is the best choice for the required sample size?
Round the result of the calculation up to the nearest whole number. To be conservative, always round up noninteger values of the calculated required sample size.
If independent samples of size n1 and n2 are drawn from normal populations with equal variances, then the value of the formula419.mml statistic is calculated as
S21/S22 The value of the test statistic for the hypothesis test of the ratio of two population variances formula415.mml is computed as formula416.mml for independent samples of size n1 and n2, with degrees of freedom formula417.mml and formula418.mml.
When examining the possible outcome of an election, what type of confidence interval is most suitable for estimating the current support for a candidate?
The confidence interval for the population proportion Sometimes the parameter of interest describes a population that is qualitative rather than quantitative. The population proportion is the essential descriptive measure of when the data type is qualitative.
Which of the following is not a restriction for comparing two population means?
The equality of the sample sizes Sample sizes need to be equal only in matched-pairs sampling.
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 Hypothesis testing is used to resolve conflicts between two competing hypotheses on a particular population parameter of interest.
We use the difference between the sample proportions formula75.mml as the point estimator of the difference between two population proportions formula76.mml
True The parameter of interest is formula77.mml where formula78.mml and formula79.mml denote the proportions in the first and second populations, respectively.
The population variance is one of the most widely used quantitative measures of risk in investments.
True With variance used as a quantitative measure of risk, an investor may want to evaluate risk in particular investment.
In an examination of holiday spending (known to be normally distributed) of a sample of 16 holiday shoppers at a local mall, an average of $54 was spent per hour of shopping. Based on the current sample, the standard deviation is equal to $21. Find a 90% confidence interval for the population mean level of spending per hour.
[$44.7967, $63.2033] Because the population standard deviation is unknown use tdf distribution. The confidence interval of the population mean is computed as formula116.mml. Use t table.
A professor applies the variance in scores between two sections that he teaches. The students of each section took the same test. The random samples drawn from the observations yield sample variances of formula460.mml = 203.15 and formula461.mml = 474.42 for samples of n1 = 13 and n2 = 16, respectively. Which of the following is a 99% confidence interval for the ratio of the population variances?
[0.1008, 2.0217]
A professor applies the variance in scores between two sections that he teaches. The students of each section took the same test. The random samples drawn from the observations yield sample variances of formula460.mml = 203.15 and formula461.mml = 474.42 for samples of n1 = 13 and n2 = 16, respectively. Which of the following is a 99% confidence interval for the ratio of the population variances?
[0.1008, 2.0217] A 100(1 - α)% confidence interval for the ratio of the population variance σ12/σ22 is computed as formula452.mml.
A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy". Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy."
[0.2116, 0.2484] A formula188.mmlconfidence interval for the population proportion p is computed as formula189.mml Use z table.
Students of two sections of a history course took a common final examination. The course instructor examines the variance in scores between the two sections. He selects random samples of n1 = 11 and n2 = 16 with sample variances of formula283.mml and formula284.mml, respectively. Assuming that the population distributions are normal, construct a 90% confidence interval for the ratio of the population variance.
[0.79, 5.70] A 100(1 − α)% confidence interval for the ratio of the population variance σ12/σ22 is computed as formula282.mml.
The result of placing a larger sample variance in the numerator of the formula402.mml test statistic allows us to
focus only on the right tail of the distribution. It is preferable to place the larger sample variance in the numerator of the formula402.mml statistic. The resulting value allows us to focus only on the right tail of the distribution.
Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune, February 26, 2011). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire in 2012, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. Which of the following should be used to develop the null and alternative hypotheses to test this claim?
p is less than or equal to 0.47, Ha: p>0.47 The competing hypotheses are Ho: p ≥ po,HA: < po. It is referred to as a left-tailed test of the population proportion.
Consider the expected returns (in percent) from the two investment options. Beth claims that the variances of the returns for the two investments differ. Use the following data to arrive at the results. Investment 1 2 −6 −4 10 8 7 5 6.5 Investment 2 5.2 −8 6 −2 5 9.5 −7 −4.5 Test Beth's claim at the 5% significance level. Which of the following is the correct conclusion?
p-value = 0.7127 >α = 0.05; Beth's claim is wrong. The decision rule is reject the null hypothesis if the p-value is less than α; do not reject the null hypothesis if the p-value is greater than α.
Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two peak hours, morning 8a.m. to 10 a.m. and evening 7p.m. to 9p.m., for the analysis. Assume that wait times are normally distributed. Wait Time (in seconds) Morning hours 8a.m.-10a.m. 97 101 115 107 129 98 96 132 118 104 123 128 95 127 112 Evening hours 7p.m.-9p.m. 95 92 89 90 102 96 85 81 84 100 97 80 98 79 99 Which of the following is the correct approximation of the p-value?
p-value lies between 0.05 and 0.10. The competing hypotheses for the two-tailed test for the population variance are formula508.mml The test statistic is computed as formula515.mml The p-value is computed as formula908.mml A point estimate of the population variance is computed as formula516.mml The values of are derived from formula517.mml using the distribution table. Because it is two-tailed test the values found in the table should be multiplied by 2.
The choice of an appropriate test for comparing two population means depends on whether we deal with _________ .
qualitative or quantitative data independent or matched-pairs sampling the equality or lack of equality of population variances All of these choices are correct Two sample hypothesis tests differ based on independence or matched-pairs, quantitative versus qualitative data, and equality of variances.
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 parameter to be tested is the mean number of customers visiting the dealership per day.
If the chosen significance level is α = 0.05, then ____________________________________________.
there is a 5% probability of rejecting a true null hypothesis The significance level is the probability of committing a Type I error, which is the probability of rejecting the null hypothesis when the null hypothesis is true.
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. Two independent samples of 25 weeks are collected for Tuesday and 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. Which of the following is the value of the appropriate test statistic?
z = -2.4736 In testing µ1 - µ2 when population variances are unknown, compute the test statistic as formula288.mml
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. In 2009, 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. The value of the test statistic is ____________.
z=-1.854 When testing the population proportion, the value of the test statistic is computed as formula54.mml
Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune, February 26, 2011). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire in 2012, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. What is the value of the appropriate test statistic to test this claim?
z = 0.721 When testing the population proportion, the value of the test statistic is computed as formula54.mml
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 with known variances and we use independent sampling. Which of the following expressions is appropriate test statistic?
z=x1-x2/sqrt(sigma^2/n1 +sigma^2/n2 With known population variances, formula173.mml and formula174.mml , the test statistic is computed as formula175.mml.
