QM
In hypothesis testing, we can reject
the null hypothesis
If a hypothesis test has a Type I error probability (α) of 0.01, it means that:
If the null hypothesis is true, you reject it 1% of the time
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the before the participants began the diet. After four weeks the participants were weighed again. What type of sampling scheme is being utilized?
Matched Pairs Sampling
Twenty participants were given a list of 20 words to study. The 20 participants were randomly assigned to one of two groups. Group 1 participants were instructed to count the number of vowels in each word (shallow processing). Group 2 participants were instructed to judge whether the object described by each word would be useful if one were stranded on a desert island (deep processing). All subjects were given a surprise free recall task. The number of words correctly recalled was recorded for each subject. What type of sampling scheme is being utilized?
Two Independent Samples
Consider the following hypotheses: H0: μ ≤ 63.4 HA: μ > 63.4 A sample of 26 observations yields a sample mean of 64.6. Assume that the sample is drawn from a normal population with a known population standard deviation of 4.0.What is the value of the test statistic? Include 2 decimal places in your answer.
1.53
A large corporation is interested in determining whether a relationship exists between the commuting time of its employees and the level of stress observed on the job. A study of 116 employees reveals the following: Stress Level Commuting Time High Moderate Low Total Less than 15 min. 9 5 18 32 15 - 45 min. 17 8 28 53 Longer than 45 min. 18 6 7 31 Total 44 19 53 116 What are the degrees of freedom used for the chi-square test of the independence of commute time and stress level?
4
In an independent samples t-test with n1 = 48 and n2 = 31, what are the degrees of freedom for the test statistic?
77
A researcher thinks that if knee surgery patients go to physical therapy twice a week (instead of the current 3 times), their recovery period will be longer. Currently, average recovery times for knee surgery patients is 8.2 weeks. What are the null and alternative hypotheses for this situation?
H0: μ μ ≤ 8.2; HA: μ μ > 8.2
24) You are testing H0: p≥0.4 against HA: p<0.4. The value of ZC is -2.38. What is the p-value of ZC? Round your answer to 4 decimal places.
.0087
In order to test H0: μ ≥ 50 HA: μ < 50. a sample of size n=43 was taken. The value of the test statistic was found to be tc = -2.08. What is the p-Value of this test statistic? Include 4 decimal places in your answer.
.0218
5) What is the value of the correlation coefficient between X and Y? Round your answer to 3 decimal places. X Y 1 58 3 63 5 55 7 72 9 67 11 75 13 80
.863
Given the following information, calculate , the pooled sample variance that should be used in the pooled-variance t test. Include 1 decimal place in your answer. n1 = 21 n2 = 31 s1 = 3 s2 = 4
13.2
19) In a random sample of 400 items, 98 are defective. If the null hypothesis is that the proportion of items that are defective is 0.20, what is the value of the test statistic used to test the null hypothesis H0: p ≤ 0.20? Include 2 decimal places in your answer.
2.25
You want to test the null hypothesis that female accounting graduates have the same average starting salary as do males. You randomly select 40 female and 40 male recent accounting graduates and obtain their starting salaries. What test is most appropriate for this situation?
Independent Samples t-test
If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to
Reject the null hypothesis
A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the auditor should conclude that there is evidence that the mean balance is different from $75, which test would you use?
T-test of Population Mean
Two or more random samples are considered independent if:
The process that generates one sample is completely separate from the process that generates the other sample.
T/F: A contingency table summarizes data that has been classified on two dimensions or scales.
True
T/F: A correlation coefficient of 0.86 indicates a strong positive linear relationship between two variables.
True
T/F: In a contingency table, when all the expected frequencies equal the observed frequencies, the calculated χ2 statistic equals zero.
True
Suppose the correlation between X and Y is 0.75. You know for a new observation that the value for X is below the mean for X. What is your best guess for the value of Y?
Y is below its mean.
A Type II error is committed when:
You don't reject a null hypothesis that is false
You are testing the null hypothesis that the average gas mileage of a mid-size car is 24 miles per gallon against the two-sided alternative. You know the population standard deviation of the gas mileage is 3. What test will you use?
Z-test for the population mean
A Type II error occurs when we:
do not reject the null hypothesis when it is actually false
A two-tailed hypothesis test of the population mean or population proportion has:
two critical values, one positive and one negative
Do graduate students study more than undergraduates? That is the question a panel of advisors wanted to answer. The panel suspects that graduate students do spend more time studying but want to test the hypothesis before making any claims. Let μ U μUbe the average number of hours per week undergraduate students spend on studying and μ G μG be the average number of hours per week graduate students spend on studying. What is the alternative hypothesis, HA?
uG-uU > 0
Given the following data table: XY 21 68 72 55 38 59 57 57 45 61 What is the correlation between X and Y? Include 3 decimal places in your answer.
-0.924
A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 95% reliable. In other words, if an individual lies, there is a 0.95 probability that the test will detect a lie. Let there also be a 0.005 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions. What is the probability of a Type II error?
.05
You are conducting a two tail hypothesis test on a population proportion. The value of Zc is -1.88. What is the p-Value of Zc? Include 4 decimal places in your answer.
.0601
Given the following information, calculate the pooled sample variance. Round your answer to 2 decimal places. s1 = 3 s2 = 5 n1 =37 n2 = 30
16.14
The χ2 statistic from a contingency table with 6 rows and 5 columns will have ____________ degrees of freedom
20
T/F: The significance level for a hypothesis test is equal to 1- β .
False
T/F: We can lower our risk of making a Type I error by increasing the sample size.
False
As a rule, the significance level of a hypothesis test is set at 0.05 unless there is justification for setting it at a different level. In a test you are conducting, if H0 is true and H0 is rejected your company will needlessly spend $10 million. Where should you set α ?
Less than 0.05
The covariance between the returns on two assets is negative. This occurs when:
On average, the return on one asset is below its expected value and the return on the other asset is above its expected value
A prominent citizen is considering a run for a U.S. Senate seat. She has decided she will run if over 50% of people who will be voting in the election view her candidacy positively. To explore how her candidacy is viewed, 400 expected voters were polled. Let p = the proportion of likely voters who view her candidacy. The null and alternative hypotheses are: H0: p ≤ 0.50. HA: p > 0.50. Which test should be used?
Z-test for the population proportion
In hypothesis testing we: a) Assume the null hypothesis is true and see if the data convince us otherwise b) Make no assumptions about the null or alternative hypothesis c) Assume the alternative hypothesis is true and see if the data convince us otherwise
a) Assume the null hypothesis is true and see if the data convince us otherwise
Which of the following would be a valid alternative hypothesis? a) The mean of a population is greater than 55. b) The mean of a population is equal to 55. c) The mean of a sample is equal to 55. d) The mean of a sample is greater than 55.
a) The mean of a population is greater than 55
In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are
n1 + n2 - 2
If the p-value is less than α in a two-tail test
the null hypothesis should be rejected.
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. Assuming the population variances are equal, what is the value of the appropriate test statistic? Include 2 decimal places in your answer.
-1.87
Six subjects took part in a weight loss study. Each subject was weighed at the beginning of the study. The subjects then completed a six-week diet and exercise plan. They were weighed after completing the plan. The results are shown below: Subject Weight Before (lbs.) Weight After (lbs.) 1 285 253 2 265 230 3 302 285 4 293 298 5 269 255 6 288 271 The variable Weight Change is defined as the Weight After minus the Weight Before. What is the average weight change? Include 1 decimal place in your answer.
-18.3
A pizza chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view. The null and alternative hypotheses tested are: H0: p ≤ 0.25 HA: p > 0.25 The value of the calculated test statistic is 2.80. What is the p-value associated with the test statistic? Include 4 decimal places in your answer.
.0026
A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 95% reliable. In other words, if an individual lies, there is a 0.95 probability that the test will detect a lie. Let there also be a 0.005 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions. What is the probability of a Type I error?
.005
18) You are conducting a one-sided test of the null hypothesis H0: p ≤ 0.5 versus the alternative hypothesis HA: p>0.5. The test statistic ZC = 2.43. What is the p-value of ZC? Include 4 decimal places in your answer.
.0075
The owner of a local nightclub has recently surveyed a random sample of n = 50 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Her null and alternative hypotheses are: H0: μ ≤ 30 HA: μ >30. The calculated value of her test statistic is 2.38. What is the p-value? Include 4 decimal places in your answer.
.0106
A biologist was interested in determining whether sunflower seedlings treated with an extract from Vinca minor roots resulted in a lower average height of sunflower seedlings than the standard height of 15.7 cm. The biologist treated a random sample of n = 33 seedlings with the extract and subsequently obtained the following heights. The biologist's hypotheses are: H0 : μ ≥ 15.7HA : μ < 15.7 The value of the test statistic used to test these hypotheses is: tc = -2.38 What is the p-value of the test statistic? Include 4 decimal places in your answer.
.0117
Suppose we wish to test H0: p = 0.80 HA: p ≠ 0.80. The value of the test statistic Zc = -2.22. What is the p-value of the test statistic? Include 4 decimal places in your answer.
.0264
In testing H0: p1 - p2 = 0 versus HA: p1 - p2 ≠ 0 You obtain a test statistic with a value of 2.18. What is the p-value? Include 4 decimal places in your answer.
.0293
When testing H0: p1 - p2 = 0 versus HA: p1 - p2 ≠ 0 , the observed value of the Zc test statistic was found to be - 2.13. The p-value for this test statistic is
.0332
16) You are conducting a t-test on the population mean based on a sample of 35 observations. The null hypothesis is H0: μ = 23. The value of the test statistic is -1.88. What is the p-value of the test statistic? Round your answer to 4 decimal places.
.0687
A local bottler in Hawaii wishes to ensure that an average of 16 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 48 bottles. The mean weight of the passion fruit juice in the sample is 15.80 ounces. Assume that the population standard deviation is 0.8 ounce. The hypotheses he uses are H0: μ = 16 HA: μ ≠ 16 The value of the test statistic is -1.73. What is the p-value of the test statistic? Include 4 decimal places in your answer.
.0902
1) You are conducting a test with the following null and alternative hypotheses: H0: p1-p2=0 Ha: p1-p2/=0 The values of the test statistic, Zc is 1.47. What is the p-value of Zc? Include 4 decimal places in your answer.
.1416
23) A company that sells home security systems wants to determine if the appeal of a new system varies between homeowners and renters. Independent samples of 140 homeowners and 60 renters were randomly selected. Each respondent viewed an ad for the new system and asked if he or she would consider purchasing the system. Of the 140 homeowners 25 indicated an interest in the new system while 9 of the 60 renters expressed an interest. Let pH be the proportion of homeowners who are interested in the system and pR be the proportion of renters. What is the value of ZC used to test the null hypothesis H0: pH - pR = 0? Round your answer to 2 decimal places.
.49
A political candidate is interested in how men view his candidacy versus how women view his candidacy. Let pM be the proportion of men who favor his candidacy and pW be the proportion of women who favor his candidacy. In a sample of 250 men 150 favored his candidacy while in a sample of 225 women 130 favored his candidacy. What is the value of the test statistic used to test the null hypothesis H0: pM - pW = 0? Include 2 decimal places in your answer.
.49
You are testing the following hypotheses using a random sample of size 38 from a normal distribution where the population standard deviation is NOT known. H0: μ ≥ 208 HA: μ < 208 The calculated value of your test statistic is 1.03. What is the p-value? Include 4 decimal places in your answer.
.8451
A manager wants to know if the mean number of defective bulbs per case is greater than 20 during the morning shift. The following is output from a computer application that does statistical test calculations: n=46 Mean=28.00 Standard Deviation=25.92 Null Hypothesis:: H0: U<=20 Alternative Hypothesis: Ha: U>20 t statistic: 2.09 What is the p-value of the test statistic?
.979
What is the largest possible value for a correlation coefficient?
1.0
A corporation randomly selects 150 salespeople and finds that 100 who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 96 out of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let p1 and p2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. What is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions? Include 2 decimal places in your answer.
1.21
A manufacturer claims that the thickness of the spearmint gum it produces is 7.5 one-hundredths of an inch. A quality control specialist regularly checks this claim. On one production run, he took a random sample of n = 40 pieces of gum and measured their thickness. The quality control specialist's hypotheses are: H0 : μ = 7.5HA : μ ≠ 7.5 The sample has a mean of 7.55 and a sample standard deviation of 0.25. What is the value of the test statistic used for evaluating these hypotheses? Include 2 decimal places in your answer.
1.26
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. What is the value of the test statistic? Include 2 decimal places in your answer.
1.68
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 and early polling results are presented next. 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 pW and pM be the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs, respectively. What is the value of the test statistic used to evaluate. the following null hypothesis? H0: pW=pM
1.74
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if a greater proportion of accounting majors hold job offers than economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," what is the value of the test H0: p1 - p2 ≤ 0 vs. HA: p1 - p2 > 0? Include 2 decimal places in your answer.
1.87
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. What is the value of the pooled estimate of the common variance? Round your answer to 1 decimal place.
12.5
If we are testing for the difference between the means of 2 related populations with samples of n1=20 and n2=20, the number of degrees of freedom is equal to
19
If we are testing for the difference between the means of 2 related populations with samples of n1=20 and n2=20, the number of degrees of freedom is equal to:
19
A professional baseball player changed his throwing motion to increase the velocity of his fastball. Before the change, the player threw his fastball at an average of 91 miles per hour. After the change in his throwing motion, the team watched him throw 64 fastballs with an average speed of 91.75 miles per hour and a sample standard deviation of 3 miles per hour. The null hypothesis for this test is H0: μ ≤ 91 vs. the one-sided alternative. What is the value of the test statistic used to determine if the average velocity on the fastball is greater than 91 mph? Include 2 decimal places in your answer.
2.00
A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Men Women Sample Size 109 52 Number Preferring Pepsi 46 13 What is the value of the test statistic used to test the null hypothesis that the proportion of men preferring Pepsi is equal to the proportion of women preferring Pepsi?
2.12
21) Suppose a sample of 30 matched pairs have an average difference of 3 and a standard deviation of 7. What is the value of the test statistic used to test the null hypothesis H0: μ D=0? Round your answer to 2 decimal places.
2.35
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. The pooled estimate of the common variance is 12.5. What is the value of the computed test statistic for testing the equality of the population means? Include 2 decimal places in your answer.
2.5
Assume that you have a sample of n1=12 and n2=15 from two independent normal populations and you wish to conduct an independent samples t-test. How many degrees of freedom does the test statistic, tc have?
25
3) The owner of a gasoline station wants to determine if the average amount of gasoline purchased by his customers is greater than 10 gallons. He randomly selects 60 customers during a certain week. This sample of 60 customers had an average amount purchased of 11.3 gallons and a standard deviation of 3.1 gallons. What is the value of tc, the test statistic used to test his hypothesis? Round your answer to 2 decimal places.
3.25
The owner of a specialty coffee shop wants to study purchasing habits of customers at her shop. She wants to determine if customers spending is different from the national average of $11.50 per visit. She selects a random sample of 60 customers during a certain week with the following results: X ¯ = 12.25, s=$1.75 What is the value of the test statistic used to evaluate customer average spending? Include 2 decimal places in your answer.
3.32
A sample of 30 paired differences yielded a sample mean of d = 5 and a sample standard deviation of 7. What is the value of the test statistic used to test the null hypothesis that the population mean difference is 0? Round your answer to 2 decimal places.
3.91
If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
38
Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test. That is the 2 independent samples t test where we can assume the populations have the same standard deviation. s1 = 4 s2 = 6 n1 = 16 n2 = 25
39
Given the following information, calculate s2p, the pooled sampled variance. s1^2=4 s2^2=6 n1=16 n2=25
5.23
The management of WXYZ wants to see if the changes made in the evening news have resulted in the proportion of the viewing audience watching WXYZ being greater than 25%. If p is the proportion of viewers watching WXYZ then H0: p ≤ 0.25 HA: p > 0.25 In a survey of 400 viewers 146 respondents indicated they watched WXYZ. What is the value of the test statistic used in conducting the test? Include 2 decimal places in your answer.
5.31
Data collected in two samples yielded the following results: s1^2=81 s2^2=36 n1=10 n2=16 What is the value of S2p?
52.88
The following table shows the cross-classification of hedge funds by market capitalization (either small, mid, or large cap)and objective (either growth or value). Growth Value Total Large Cap 23 19 42 Mid Cap 9 10 19 Small Cap 17 72 89 Total 49 101 150 What are the degrees of freedom for testing the null hypothesis that market capitalization is independent of objective?
6
Two populations are known to have the same population variance. Data from two independent samples of size 30 yielded sample standard deviations of 2 and 3. What is the value of the pooled estimate of the common variance? Include 1 decimal place in your answer.
6.5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Student Exam Score Before Course Exam Score After Course 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 The number of degrees of freedom for the test of the effectiveness of the course is:
7
Given the following information, calculate , the pooled sample variance that should be used in the pooled-variance t test. Include 2 decimal places in your answer. n1 = 16 n2 = 25 s^2 1= 6 s^2 2= 9
7.85
8) You are testing the means of two independent samples using a pooled variance t-test. Sample 1 has 30 observations and a sample variance of 10. Sample 2 has 40 observations and a sample variance of 8. What is the pooled estimate of the common variance used in constructing tc? Round your answer to 2 decimal places.
8.85
A piece of machinery at a manufacturing facility has been set to produce bolts that are an average of 1.5 inches in length. Overnight a mouse crept into the machine and bumped a sensitive piece. The machine is actually producing bolts with an average length of 1.6 inches. A routine quality control sample taken the next day did not reject the null hypothesis that the machine was producing bolts with an average length of 1.5 inches. What happened here?
A Type 2 Error was made
A cereal packing machine is set to fill boxes with an average of 25 ounces of cereal. Periodically, 30 filled boxes are selected at random and the contents weighed. A t-test is then conducted to test the null hypothesis H0: against the two-sided alternative. On the last check, the null hypothesis was rejected even though the machine was packing an average of 25 ounces. What has happened?
A Type I Error has occurred
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 and early polling results are presented next. 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?
A Z-test of two population proportions with a zero hypothesized difference.
You are testing the null hypothesis H0: p = 0.30 against the two-tail alternative hypothesis HA: p ≠ 0.30 and you choose the level of significance to be = 0.01. The value of your test statistic Zc = 2.15. What is your decision?
Do Not Reject H0
In order to test H0: p1 - p2 = 0 versus HA: p1 - p2 ≠ 0, a Z-test of two independent proportions was conducted with α = 0.05. The p-Value of the test statistic was 0.08. What is your decision?
Do not reject H0
You are conducting a matched samples t-test on the average difference between the populations at the 0.05 level of significance. The p-value for tc is found to be 0.23. What is your decision?
Do not reject H0
T/F: Expected cell frequencies for a contingency table are calculated by assuming statistical dependence.
False
T/F: If two samples have the same number of observations, a matched samples t-test will give the same result as an independent samples t-test.
False
T/F: The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.
False
The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are:
H0: U<=30, Ha: U>30
Researchers determined that 60 tissues is the mean number of tissues used during a cold. Product engineers at Kimberly Clark Corporation have developed a more absorbent tissue that they feel will lower the average number of tissues needed. If the engineers' claims are substantiated Kimberly Clark will aggressively promote this benefit. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.
H0: U>=60, Ha: U<60
A pizza chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view. State the test of hypothesis that is of interest to the pizza chain.
H0: p ≤ 0.25; HA: p>0.25
Consolidated Power, a large electric power utility, has just built a modern nuclear power plant. This plant discharges waste water that is allowed to flow into the Atlantic Ocean. The Environmental Protection Agency (EPA) has ordered that the waste water may not be excessively warm so that thermal pollution of the marine environment near the plant can be avoided. Because of this order, the waste water is allowed to cool in specially constructed ponds and is then released into the ocean. This cooling system works properly if the mean temperature of waste water discharged is 60°F or cooler. Consolidated Power is required to monitor the temperature of the waste water. A sample of 100 temperature readings will be obtained each day, and if the sample results cast a substantial amount of doubt on the hypothesis that the cooling system is working properly, then the plant must be shut down and appropriate actions must be taken to correct the problem.
H0: u<=60, Ha: U>60
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and under filling bottles are undesirable: Under filling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, µ, is close to the target fill of 16 ounces. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 16 ounces, then the filler's initial setup will be readjusted. What are the null and alternative hypotheses for this hypothesis test.
H0: u=16, Ha: u/=/16
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;
A demographer wants to measure life expectancy in countries 1 and 2. Let μ 1 and μ 2 denote the mean life expectancy in countries 1 and 2, respectively. Specify the hypothesis to determine if life expectancy in country 1 is more than 10 years lower than in country 2.
H0: μ 1 - μ 2 ≥ -10; HA: μ 1 - μ 2 < -10
A bank manager has developed a new system to reduce the time customers spend waiting for teller services during peak hours. The manager hopes the new system will reduce waiting times from the current average of 9 minutes to less than 6 minutes. If we define μ as the mean waiting time under the new system, what are the null and alternative hypotheses to evaluate the claim that the average wait time is less than 6 minutes?
H0: μ ≥ 6; HA: μ < 6
A large telemarketing company is considering a new training method. The new method has additional costs. The company will adopt the new method if the sales rate can be shown to be more than 5% higher than the current method. To determine this, the company divided its sales force of 1,000 into 2 groups. Group 1 was trained with the current method. Group 2 was trained using the new method. Let p1 be the sales rate for Group 1 and p2 be the sales rate for Group 2. What is HA, the alternative hypothesis for this test?
HA: p2-p1>0.05
The U.S. Department of Education reports that 40% of full-time college students are employed while attending college. An advisor at a university wanted to conduct a study to determine if the proportion of students at her university is different from this national average. If p is the proportion of students at her university who are employed, what is the alternative hypothesis, HA in her hypothesis test?
HA: p=/ 0.4
A drug manufacturer will claim that it's drug, Headache-B-Gone (HBG) is more effective in treating headaches than a competitor's drug, Bye-Bye Migraine (BBM) if it can show that HBG provides relief in more than 5% more cases than BBM. To test this claim 300 headache sufferers were randomly placed in two groups. One group was given HBG to treat a headache while the other was given BBM. Let pH be the proportion of headache sufferers in Group 1 who got relief using HBG and pB be the proportion of headache sufferers in Group 2 who got relief using HBG. What is the appropriate alternative hypothesis for this test?
HA: pH - pB > 0.05
A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50-milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage. What is the alternative hypothesis used to test if the machine is producing, on average, 50-milligram doses or if the average doses are different from 50-milligrams? Let be the average dose.
Ha: U=/ 50
National Paper Company must purchase a new machine for producing cardboard boxes. The company has narrowed its choices to 2 machines. The two machines are comparable in price and the quality of boxes produced so the company is going to choose the machine that produces, on average, more boxes. It is known that there are significant differences in the abilities of the machine operators. Because of this difference the company has chosen 10 operators to conduct a test. Each operator will operate Machine 1 for 4 hours and Machine 2 for another 4 hours. This is an example of what kind of sampling?
Matched Pairs
You want to compare grocery prices at Publix and Walmart. To do this you develop a shopping list of 30 items that are sold in both stores. After pricing these 30 items at both stores you then conduct a hypothesis test to test the null hypothesis that the average price for these items is the same at both stores vs. the alternative hypothesis that the average price is not equal. What test is most appropriate for this situation?
Matched Pairs T-test
A class of 25 police trainees were seated in a darkened room facing a projector screen. Ten different license planes were projected on the screen, one at a time, for 5 seconds each, separated by 15-second intervals. After the last 15-second interval, the lights were turned on and the police trainees were asked to write down as many of the 10 license plate numbers they can. After a week-long memory training course, the trainees were shown 10 new license plates and retested. What type of sampling scheme is being utilized?
Matched-Pair Sampling
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample Size 211 200 Sample Mean SSATL Score 65.75 79.83 Sample Standard Deviation 11.07 6.41 Which test should be used?
Pooled-variance t-test for the difference between two means
You are conducting a hypothesis test and have set α equal to 0.05. The p-Value of your test statistic is 0.0023. What is your decision?
Reject H0
You are conducting a two independent samples t-test of the population means with a two-sided HAwith =0.05. The sample sizes are n1=35 and n2=45. The p-value of your test is 0.003. What is your decision?
Reject H0
A study of the effect of caffeine on muscle metabolism used eighteen male volunteers who each underwent arm exercise tests. Nine of the men were randomly selected to take a capsule containing pure caffeine one hour before the test. The other men received a placebo capsule. During each exercise the subject's respiratory exchange ratio (RER) was measured. (RER is the ratio of CO2 produced to O2 consumed and is an indicator of whether energy is being obtained from carbohydrates or fats). The question of interest to the experimenter was whether, on average, caffeine changes RER. The two populations being compared are "men who have not taken caffeine" and "men who have taken caffeine". What type of sampling scheme is being utilized?
Two Independent Samples
The use of preservatives by food processors has become a controversial issue. Suppose two preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 40 cuts of fresh meat are treated with preservative I and 35 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 75 cuts of meat. What type of sampling scheme is being utilized?
Two Independent Samples
A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids."
Type I: 4%, Type II: 6%
When interpreting the covariance between variables x and y, which of the following statements is the most accurate? a) A negative value of covariance indicates that, on average, if x is above its mean, then y tends to be above its mean. b) A negative value of covariance indicates that, on average, if x is below its mean, then y tends to be below its mean. c) A positive value of covariance indicates that, on average, if x is below its mean, then y tends to be below its mean. d) A positive value of covariance indicates that, on average, if x is above its mean, then y tends to be below its mean.
c) A positive value of covariance indicates that, on average, if x is below its mean, then y tends to be below its mean
Which of the following is a valid null hypothesis? a) The population proportion is less than 0.65. b) The sample proportion is less than 0.65. c) The population proportion is not less than 0.65. d) The sample proportion is not less than 0.65.
c) The population proportion is not less than 0.65
When conducting a chi-square test of independence in a contingency table, as the difference between observed frequency and expected frequency _______________, the probability of rejecting the null hypothesis increases.
increases
For the chi-square test of a contingency table, the expected cell frequencies are found as:
the row total multiplied by the column total divided by the sample size
If the chosen significance level is α = 0.05, then:
there is a 5% probability of rejecting a true null hypothesis
A Type I error is committed when:
you reject a null hypothesis that is true.
The owner of a large car dealership believes that the closing of two local businesses has decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. She decides to test the null hypothesis that the average number of customers is at least 800 vs. the alternative hypothesis that the average number of customers is less than 800. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. The population standard deviation is known to be 350. What is the value of the test statistic she should use for this test? Include 2 decimal places in your answer.
-1.43
A pharmaceutical industry survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test the claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. What is the value of the test statistic used in evaluating this claim? Include 2 decimal places in your answer.
-2.33
