Q&A Hero

Q: The degrees of freedom for a contingency table with 6 rows and 3 columns is a. 18 b. 15 c. 6 d. 10

Q: The degrees of freedom for a contingency table with 12 rows and 12 columns is a. 144 b. 121 c. 12 d. 120

Q: A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a a. contingency test b. probability test c. goodness of fit test d. None of these alternatives is correct.

Q: In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be a. at least 5 b. at least 10 c. no more than 5 d. less than 2

Q: The number of degrees of freedom for the appropriate chi-square distribution in a test of independence isa. n -1b. k-1c. number of rows minus 1 times number of columns minus 1d. a chi-square distribution is not used

Q: An important application of the chi-square distribution is a. making inferences about a single population variance b. testing for goodness of fit c. testing for the independence of two variables d. All of these alternatives are correct.

Q: A goodness of fit test is always conducted as a a. lower-tail test b. upper-tail test c. middle test d. None of these alternatives is correct.

Q: The sampling distribution for a goodness of fit test is the a. Poisson distribution b. tdistribution c. normal distribution d. chi-square distribution

Q: A population where each element of the population is assigned to one and only one of several classes or categories is a a. multinomial population b. Poisson population c. normal population d. None of these alternatives is correct.

Q: Which of the following does notneed to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. All of the information provided is necessary.

Q: In a two-tailed hypothesis test the test statistic is determined to be z= -2.5. The p-value for this test a. is 0.0062 b. is 0.0124 c. is 0.4938 d. cannot be determined, since the level of confidence is not given.

Q: If the p-value is less than ,a. the alternative hypothesis is rejectedb. the null hypothesis is rejectedc. the null hypothesis will sometimes be rejected and sometimes not be rejected depending on the sample sized. Not enough information is given to answer this question.

Q: If a hypothesis is rejected at 95% confidence, a. it must also be rejected at the 99% confidence b. it must also be rejected at the 90% confidence c. it will sometimes be rejected and sometimes not be rejected at the 90% confidence d. Not enough information is given to answer this question.

Q: The sampling distribution of is approximated by a a. normal distribution b. tdistribution with n1+ n2degrees of freedom c. t distribution with n1+ n2" 1 degrees of freedom d. tdistribution with n1+ n2+ 2 degrees of freedom

Q: Assume we are interested in determining whether the proportion of voters planning to vote for candidate C (pC) is significantly lessthan the proportion of voters planning to vote for candidate B (pB). The correct null hypothesisfor testing the above isa. Ho: pC-pB0b. Ho: pC-pB< 0c. Ho: pC-pB0d. Ho: pC-pB0

Q: If we are interested in testing whether the proportion of items in population 1 is largerthan the proportion of items in population 2, thea. null hypothesis should state p1-p2> 0b. null hypothesis should state p1-p20c. alternative hypothesis should state p1-p2>0d. alternative hypothesis should state p1-p2<0

Q: The purpose of the hypothesis test for proportions of a multinomial population is to determine whether the actual proportions a. are all equal b. follow a normal distribution c. are different than the hypothesized proportions d. follow a chi-square distribution

Q: Both the hypothesis test for proportions of a multinomial population and the test of independence focus on the difference between a. sample means and population means b. observed frequencies and expected frequencies c. two population proportions d. two interval estimates

Q: The assumptions for the multinomial experiment parallel those for the binomial experiment with the exception that for the multinomial a. there are more trials b. the probability of each outcome can change from trial to trial c. there are three or more outcomes per trial d. the trials are not independent

Q: The test for goodness of fit a. is always a one-tail test with the rejection region occurring in the upper tail b. is always a one-tail test with the rejection region occurring in the lower tail c. is always a two-tail test d. can be a one-tail or two-tail test

Q: Both the hypothesis test for proportions of a multinomial population and the test of independence employ the a. Fdistribution b. tdistribution c. normal distribution d. chi-square distribution

Q: The test statistic for the chi-square tests in our textbook requires, for each category, an expected frequency of at least a. 2 b. 5 c. 10 d. 30

Q: In conducting a hypothesis test about p1- p2, any of the following approaches can be used excepta. comparing the observed frequencies to the expected frequenciesb. comparing the p-value to c. comparing the hypothesized difference to the confidence intervald. comparing the test statistic to the critical value

Q: In the case of the test of independence, the number of degrees of freedom for the appropriate chi-square distribution is computed asa. k-1b. k-2c. (r- 1)(c- 1)d. rc-2

Q: The properties of a multinomial experiment include all of the following except a. the experiment consists of a sequence of nidentical trials b. three or more outcomes are possible on each trial c. the probability of each outcome can change from trial to trial d. the trials are independent

Q: The test of independence presented in our textbook requires that there be a. two variables, each having two outcomes b. two variables, each having two or more outcomes c. two or more variables, each having two outcomes d. two or more variables, each having two or more outcomes

Q: City planners are evaluating three proposed alternatives for relieving the growing traffic congestion on a north-south highway in a booming city. The proposed alternatives are: (1) designate high-occupancy vehicle (HOV) lanes on the existing highway, (2) construct a new, parallel highway, and (3) construct a light (passenger) rail system.In an analysis of the three proposals, a citizen group has raised the question of whether preferences for the three alternatives differ among residents near the highway and non-residents. A test of independence will address this question, with the hypotheses being:H0: Proposal preference isindependent of the residency status of the individualHa: Proposal preference is notindependent of the residency status of the individualA simple random sample of 500 individuals has been selected. The crosstabulation of the residency statuses and proposal preferences of the individuals sampled is shown below.Residency StatusHOV LaneNew HighwayLight RailNearby resident1104570Distant resident1407560Conduct a test of independence using = .05 to address the question of whether residency status is independent of the proposal preference.

Q: Refer to Exhibit 10-4. The 95% confidence interval for the difference between the two population means isa. -5.372 to 11.372b. -5 to 3c. -4.86 to 10.86d. -2.65 to 8.65

Q: Refer to Exhibit 10-4. The degrees of freedom for the tdistribution are a. 22 b. 21 c. 20 d. 19

Q: Refer to Exhibit 10-4. The standard error of is a. 3.0 b. 4.0 c. 8.372 d. 19.48

Q: Exhibit 10-4The following information was obtained from independent random samples.Assume normally distributed populations with equal variances.Sample 1Sample 2Sample Mean4542Sample Variance8590Sample Size1012Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations isa. 0b. 2c. 3d. 15

Q: Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)a. There is a statistically significant difference in the average final examination scores between the two classes.b. There is no statistically significant difference in the average final examination scores between the two classes.c. It is impossible to make a decision on the basis of the information given.d. There is a difference, but it is not significant.

Q: Refer to Exhibit 10-3. The p-value for the difference between the two population means is a. .0014 b. .0027 c. .4986 d. .9972

Q: Refer to Exhibit 10-3. The test statistic for the difference between the two population means is a. -.47 b. -.65 c. -1.5 d. -3

Q: Refer to Exhibit 10-3. The 95% confidence interval for the difference between the two population means is a. -9.92 to -2.08 b. -3.92 to 3.92 c. -13.84 to 1.84 d. -24.228 to 12.23

Q: Refer to Exhibit 10-3. The standard error of is a. 12.9 b. 9.3 c. 4 d. 2

Q: Exhibit 10-3A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.TodayFive Years Ago8288112.554n4536Refer to Exhibit 10-3. The point estimate for the difference between the means of the two populations isa. 58.5b. 9c. -9d. -6

Q: Refer to Exhibit 10-2. Thea. null hypothesis should be rejectedb. null hypothesis should not be rejectedc. alternative hypothesis should be acceptedd. None of these alternatives is correct.

Q: Refer to Exhibit 10-2. The null hypothesis to be tested is H0: md= 0. The test statistic is a. -1.96 b. 1.96 c. 0 d. 1.645

Q: Exhibit 10-2The following information was obtained from matched samples.The daily production rates for a sample of workers before and after a training program are shown below.WorkerBeforeAfter12022225233272742320522256201971718Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations isa. -1b. -2c. 0d. 1

Q: Refer to Exhibit 10-1. At 95% confidence, the conclusion is thea. average salary of males is significantly greater than femalesb. average salary of males is significantly lower than femalesc. salaries of males and females are equald. None of these alternatives is correct.

Q: Refer to Exhibit 10-1. The p-value is a. 0.0668 b. 0.0334 c. 1.336 d. 1.96

Q: Refer to Exhibit 10-1. If you are interested in testing whether or not the average salary of males is significantly greater than that of females, the test statistic is a. 2.0 b. 1.5 c. 1.96 d. 1.645

Q: Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is a. 0 to 6.92 b. -2 to 2 c. -1.96 to 1.96 d. -0.92 to 6.92

Q: Refer to Exhibit 10-1. At 95% confidence, the margin of error is a. 1.96 b. 1.645 c. 3.920 d. 2.000

Q: Refer to Exhibit 10-1. The standard error for the difference between the two means is a. 4 b. 7.46 c. 4.24 d. 2.0

Q: Exhibit 10-1Salary information regarding male and female employees of a large company is shown below.MaleFemaleSample Size6436Sample Mean Salary (in $1,000)4441Population Variance12872Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations isa. -28b. 3c. 4d. -4

Q: In an analysis of variance, one estimate of 2is based upon the differences betweenthe treatment means and thea. means of each sampleb. overall sample meanc. sum of observationsd. populations have equal means

Q: Which of the following is nota required assumption for the analysis of variance? a. The random variable of interest for each population has a normal probability distribution. b. The variance associated with the random variable must be the same for each population. c. At least 2 populations are under consideration. d. Populations have equal means.

Q: An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of Fare a. 3 and 30 b. 4 and 30 c. 3 and 119 d. 3 and 116

Q: The critical Fvalue with 8 numerator and 29 denominator degrees of freedom at= 0.01 isa. 2.28b. 3.20c. 3.33d. 3.64

Q: An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of Fare a. 5 and 20 b. 4 and 20 c. 4 and 99 d. 4 and 95

Q: In a completely randomized design involving four treatments, the following information is provided.Treatment 1Treatment 2Treatment 3Treatment 4Sample Size50181517Sample Mean32384248The overall mean (the grand mean) for all treatments isa. 40.0b. 37.3c. 48.0d. 37.0

Q: In a completely randomized design involving three treatments, the following information is provided:Treatment 1Treatment 2Treatment 3Sample Size5105Sample Mean489The overall mean for all the treatments isa. 7.00b. 6.67c. 7.25d. 4.89

Q: In order to determine whether or not the means of two populations are equal, a. at test must be performed b. an analysis of variance must be performed c. either at test or an analysis of variance can be performed d. a chi-square test must be performed

Q: A term that means the same as the term "variable" in an ANOVA procedure is a. factor b. treatment c. replication d. variance within

Q: In ANOVA, which of the following is not affected by whether or not the population means are equal?a. b. between-samples estimate of 2c. within-samples estimate of 2d. None of these alternatives is correct.

Q: An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of Fare a. 3 and 20 b. 3 and 16 c. 4 and 17 d. 3 and 19

Q: The required condition for using an ANOVA procedure on data from several populations is that the a. the selected samples are dependent on each other b. sampled populations are all uniform c. sampled populations have equal variances d. sampled populations have equal means

Q: In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is a. 200 b. 40 c. 80 d. 120

Q: The standard error of is the a. variance of b. variance of the sampling distribution of c. standard deviation of the sampling distribution of d. difference between the two means

Q: If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means a. can be approximated by a Poisson distribution b. will have a variance of one c. can be approximated by a normal distribution d. will have a mean of one

Q: Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known. The sample sizes are n1= 25 and n2= 35. The correct distribution to use is the a. Poisson distribution b. tdistribution with 60 degrees of freedom c. tdistribution with 59 degrees of freedom d. tdistribution with 58 degrees of freedom

Q: Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known. The sample sizes are n1= 32 and n2= 40. The correct distribution to use is the a. binomial distribution b. tdistribution with 72 degrees of freedom c. tdistribution with 71 degrees of freedom d. tdistribution with 70 degrees of freedom

Q: When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as a. corresponding samples b. matched samples c. independent samples d. None of these alternatives is correct.

Q: To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown, we must use a tdistribution with (let n1be the size of sample 1 and n2the size of sample 2)a. (n1+ n2) degrees of freedomb. (n1+ n2-1) degrees of freedomc. (n1+ n2-2) degrees of freedomd. n1-n2+ 2

Q: When developing an interval estimate for the difference between two sample means, with sample sizes of n1and n2, a. n1must be equal to n2 b. n1must be smaller than n2 c. n1must be larger than n2 d. n1and n2can be of different sizes

Q: If we are interested in testing whether the mean of population 1 is significantly smaller than the mean of population 2, thea. null hypothesis should state 1-2< 0b. null hypothesis should state 1-20c. alternative hypothesis should state 1-2< 0d. alternative hypothesis should state 1-2> 0

Q: If we are interested in testing whether the mean of population 1 is significantly larger than the mean of population 2, thea. null hypothesis should state 1-2> 0b. null hypothesis should state 1-20c. alternative hypothesis should state 1-2>0d. alternative hypothesis should state 1-2<0

Q: If we reject the hypothesis H0: 1= 2= 3, we can conclude thata. all three population means are similarb. all three population means are equalc. all three population means are differentd. at least two population means are different

Q: In analysis of variance, the dependent variable is called the a. response variable b. factor c. experimental unit d. design variable

Q: In analysis of variance, the independent variable of interest is called the a. response variable b. factor c. experimental unit d. design variable

Q: In analysis of variance, the levels of the factor are called the a. dependent variables b. experimental units c. treatments d. observations

Q: The process of using the same or similar experimental units for all treatments in order to remove a source of variation from the error term is called a. replicating b. partitioning c. randomizing d. blocking

Q: The process of allocating the total sum of squares and degrees of freedom to the various components is referred to as a. replicating b. partitioning c. randomizing d. blocking

Q: If we are testing for the equality of 3 population means, we should use thea. test statistic tb. test statistics zc. test statistic 2d. test statistic F

Q: The within-treatments estimate of 2is called thea. sum of squares due to errorb. mean square due to errorc. sum of squares due to treatmentsd. mean square due to treatments

Q: In testing for the equality of kpopulation means, the number of treatments isa. kb. k-1c. nTd. nT-k

Q: The test statistic Fis the ratio a. MSE/MST b. MSTR/MSE c. SSTR/SSE d. SSTR/SST

Q: In making three pairwise comparisons, what is the experiment-wise Type I error rate ewif the comparison-wise Type I error rate is .10?a. .001b. .081c. .271d. .300