stats 9, stats 8, STATS 7, stats

The​ P-value for a hypothesis test is 0.073. For each of the following significance​ levels, decide whether the null hypothesis should be rejected.

.05 - do not reject the null hypothesis because the​ P-value is greater than the significance level. 0.10 - Reject the null hypothesis because the​P-value is equal to or less than the significance level.

Can pleasant smells improve​ learning? Researchers timed 21 subjects as they tried to complete​ paper-and-pencil mazes. Each subject attempted a maze both with and without the presence of a floral aroma. Subjects were randomized with respect to whether they did the scented trial first or second. Suppose a paired​ t-test is to be performed to determine whether there is evidence to indicate that the time to complete the maze is faster in scented trials compared to unscented​ trials, on average. The summary statistics for the difference in time to complete the maze​ (in seconds) between the unscented and scented trials ​(unscented− scented) are x=3.85 and s=13.01. How many degrees of freedom does the​ t-statistic have?

20 The paired​ t-test is a​ one-sample t-test on the differences. A​ one-sample t-test has n−1 degrees of​ freedom, where n is the number of pairs or the number of differences. Since there are 21 differences in this​ problem, the test has 20 degrees of freedom.

errors

A Type I error is rejecting a true null​ hypothesis, whose probability is denoted α. A Type II error is not rejecting a false null​ hypothesis, whose probability is denoted β.

Type II Error

A Type II Error is made when​ there's not enough evidence to reject the null​ hypothesis, but the null hypothesis is not true.

Which of the following is a correct explanation of what a confidence interval​ is?

A confidence interval is a range of values used to estimate the true value of a population parameter. The confidence level is the probability the interval actually contains the population​ parameter, assuming that the estimation process is repeated a large number of times.

A larger population standard deviation

A larger population standard deviation decreases power.

​(a) A larger predicted difference between the means of the populations

A larger predicted difference between the means of the populations increases power

A larger sample size

A larger sample size increases power.

The means for the​ moderate-stereotype group are less than the means for the​ extreme-stereotype group for both​ conditions, which indicates an effect for stereotype group.

A marginal mean in a factorial design in analysis of variance is the mean score for all the participants at a particular level of one of the grouping variables. There is a main effect for a particular grouping variable if the marginal means for the different levels of that grouping variable are not the same. Since the sum of the heights of the bars for each stereotype group are not the same because the heights of the bar for the​ extreme-stereotype group are greater than the heights of the bars for the​ moderate-stereotype group for both​ conditions, there seems to be a large effect for stereotype​ group, which the ANOVA results confirm

For the following​ study, say whether you would use a t test for dependent means or a t test for independent means. A researcher measures the resting heart rate of a group of 25 patients before and after they take a particular drug.

A. A t test for dependent means should be​ used, because the two sets of scores are from a single group of people.

An investigator conducts an experiment with four treatment groups. The response variable is growth of a plant during the experiment. She performs an​ F-test. What is the null hypothesis the researcher is testing with the​ F-test?

All four treatment groups have the same average growth of the plants during the experiment.

An investigator conducts an experiment with four treatment groups. The response variable is growth of a plant during the experiment. She performs an​ F-test. What is the alternative hypothesis the researcher is testing with the​ F-test?

At least one treatment group has a different average growth of plants during the​ experiment, but not all four necessarily have different mean growths.

There is some concern that if a woman has an epidural to reduce pain during​ childbirth, the drug can get into the​ baby's bloodstream, making the baby sleepier and less willing to breastfeed. A Journal published results of a study conducted at a university. Researchers followed up on 1184 ​births, noting whether the mother had an epidural and whether the baby was still nursing after 6 months. The results are shown to the right.

A​ chi-square test for independence These data differ from other kinds of data because they categorize subjects from a single group on two categorical variables rather than on only one. A​ chi-square test for independence is used here. ​State the null and alternative hypotheses. H0:Breastfeeding sucess is independent of having an epidural. Ha:There's an association between breastfeeding success and having an epidural.

A​ p-value is the probability​ _____________.

A​ p-value is the probability of observing the actual​ result, a sample​ mean, for​ example, or something more unusual just by chance if the null hypothesis is true.

A data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and​ glass? Use a significance level of α=0.05.

Because the absolute value of the test statistic is less than or equal to the positive critical​ value, there is not sufficient evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α=0.05.

A scientist investigated the effect of​ cross-fertilization on the heights of plants. In one​ study, the scientist planted 15 pairs of a species of plant. Each pair consisted of one​ cross-fertilized plant and one​ self-fertilized plant grown in the same pot. The accompanying table gives the height​ differences, in eighths of an​ inch, for the 15 pairs. Each difference is obtained by subtracting the height of the​ self-fertilized plant from that of the​ cross-fertilized plant

Calculate​ t-obtained t=2.04 The​ t-critical values are - 2.98 , 2.98 What is the conclusion for the hypothesis​ test? Do not reject H0​; the data do not provide sufficient evidence at the 1​% significance level that the mean heights differ.

A researcher drilled a hole in a die and filled it with a lead​ weight, then proceeded to roll it 201 times. The observed frequencies for the outcomes of​ 1, 2,​ 3, 4,​ 5, and 6 respectively are 37​, 29​, 39​, 35​, 33​, and 28. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair​ die?

Determine the null and alternative hypotheses H0​: All outcomes are equally likely. Ha​: At least one of the probabilities is different from the others

The​ P-value is .363 test at the 10​% significance level.

Do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean is not equal to 34.

2x4 ANOVA. Which of the following would be an appropriate research conclusion if the interaction null hypothesis was​ rejected?

Evidence suggests an interaction between Variable A and Variable B.

Which of the following is a correct report of a​ two-sample t-test​ (alpha =​ .05) in which the null hypothesis was​ REJECTED?

Evidence suggests that Group A had a higher mean than Group B on Outcome​ X, ​t(32) =​ 4.82, p​ < .05.

Researchers conducted a study and obtained a​ p-value of 0.75. Based on this​ p-value, what conclusion should the researchers​ draw?

Fail to reject the null hypothesis but do not accept the null hypothesis as true either.

The accompanying data provide the​ weights, in​ pounds, of 17 anorexic women before and after receiving a therapy treatment for anorexia nervosa. Find a​ 90% confidence interval for the weight gain that would be​ obtained, on​ average, by using the family therapy treatment.

Find the​ 90% confidence interval. Use Before−After. −10.29,−4.24 pounds We can be​ 90% confident that the weight gain that would be​ obtained, on​ average, by using the family therapy treatment is somewhere between the endpoints of the confidence interval.

For a given degrees of​ freedom, the larger the​ chi-square statistic, the​ ____________ evidence there is to reject the null hypothesis.

For a given degrees of​ freedom, the larger the​ chi-square statistic, the more evidence there is to reject the null hypothesis. Larger differences between the observed and expected counts lead to more evidence to reject the null hypothesis. Larger differences between observed and expected counts will also lead to larger​ chi-square statistics.

A distribution and the observed frequencies of the values of a variable from a simple random sample of the population are provided below. Use the​ chi-square goodness-of-fit test to​ decide, at the specified significance​ level, whether the distribution of the variable differs from the given distribution. ​Distribution: 0.125​, 0.25​, 0.25​, 0.375 Observed​ frequencies: 19​, 21​, 21​, 35 Significance level=0.05

H0​: The distribution of the variable is the same as the given distribution. Ha​: The distribution of the variable differs from the given distribution.

A researcher developing scanners to search for hidden weapons at airports has concluded that a new scanner is significantly better than the current scanner. He made his decision based on a test using α=0.05. Would he have made the same decision at α=0.20? How about α=0.001?

His decision would have been the same for α=0.20 but may have been different for α=0.001.

Which of the following are mistakes that can be made in a hypothesis​ test? I. H0 is​ true, and we reject it. II. H0 is​ true, and we fail to reject it. III.H0 is​ false, and we fail to reject it

I and III

Is ρ a parameter or a​ statistic?

It is a parameter because ρ is a descriptive measure for a population.

Is r a parameter or a​ statistic?

It is a statistic because r is a descriptive measure for a sample.

2x4 ANOVA. When reporting the results for a twoway​ ANOVA, it is important include not just the reports of the F and​ p-values but also​ the:

MSE

A professor wondered whether grades on her midterm predicted​ (i.e., were related​ to) grades on her final. Assume both grades are​ quantitative/numeric.

Pearson r

Power

Power is the probability that a hypothesis test will correctly reject a false null hypothesis.

If we use the amounts​ (in millions of​ dollars) grossed by movies in categories with​ PG, PG-13, and R​ ratings, we obtain the SPSS analysis of variance results shown below. Use a 0.01 significance level to test the claim that PG​ movies, PG-13​ movies, and R movies have the same mean gross amount.

Reject H0. There is sufficient evidence to warrant rejection of the claim that PG​movies, PG-13​movies, and R movies have the same mean gross amount.

A​ 95% confidence interval for μ1−μ2 using the​ two-sample t-methods with 35 degrees of freedom is ​(−​3,7).

SE(x1−x2)= 2.4631 The notation SEx1−x2 is for the standard error of the distribution of the difference in sample means. Since the margin of error is 5 and t* with 35 degrees of freedom is​ 2.030, the following is true. SE(x1−x2) = 52.030= 2.4631

SSE

SSE is the error sum of squares. It represents the variation within the samples. SSwithin

SST

SST is the total sum of squares. It represents the total variation among all the sample data.

SSTR

SSTR is the treatment sum of squares. It represents the variation among the sample means. SSbetween

Jan performed a study and obtained a​ p-value of 1.24. What conclusion should Jan​ make?

She made an error since it is not possible to get a​ p-value of 1.24.

Which of the following is NOT true when using​ one-way analysis of variance for testing equality of three or more population​ means?

Small F test statistics indicate that the decision is to reject the null hypothesis of equal means.

Which of the following is NOT a property of the F​ distribution?

The F distribution is bell shaped.

A​ 95% confidence interval for μ1−μ2 using the​ two-sample t methods with 40 degrees of freedom is​ (65,71).

The margin of error is 3.

The American Association of University Professors​ (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. Independent simple random samples of 35 faculty members in private institutions and 30 faculty members in public institutions yielded the annual​ salaries, in thousands of​ dollars, displayed in Data set 1. At the​ 5% significance​ level, do the data provide sufficient evidence to conclude that mean salaries for faculty in private and public institutions​ differ? Apply the pooled​ t-test.

The null hypothesis for this hypothesis test is H0​: µ1=µ2. ​However, H0​: μ1−μ2=0 is an equivalent way of writing the same null hypothesis.

The American Association of University Professors​ (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. Independent simple random samples of 35 faculty members in private institutions and 30 faculty members in public institutions yielded the annual​ salaries, in thousands of​ dollars, displayed in Data set 1. At the​ 5% significance​ level, do the data provide sufficient evidence to conclude that mean salaries for faculty in private and public institutions​ differ? Apply the pooled​ t-test.

The null hypothesis is H0: μ1=μ2. The alternative hypothesis is is HA: μ1 not= μ2.

An experiment is conducted in which 68 participants each fill out a personality​ test, but not according to the way the participants see themselves.​ Instead, 17 are randomly assigned to fill it out according to the way they think their mothers see​ them; 17 as their fathers would fill it out for​ them; 17 as their best friends would fill it out for​ them; and 17 as the professors they know best would fill it out for them. The main results appear in the accompanying table. Explain these results to a person who has never had a course in statistics.

The null hypothesis is that the groups Mother, Father, Friend, and Professor are from populations of main personality scales with equal means. There are four such​ hypotheses, one each for Conformity, Extroversion, Maturity, and Self-Confidence. If the null hypothesis is true, the variance of these populations can be estimated in two ways.​ (i) Estimate from the variation within each of the four groups and then average them.​ (ii) Estimate from the variation between the four​ means, multiplying by the size of each sample group. Since the estimates should be approximately​ equal, the ratio of the two estimates should be approximately 1. If the null hypothesis is false, the estimate​ (ii) is greater than the estimate​ (i) and the​ ratio, F, of​ (i) to​ (ii) is greater than 1. The fact that F=4.27 is much larger than 1 and p<0.01 indicates that the null hypothesis for Conformity can be rejected. The fact that F=2.05 is not much larger than 1 indicates that the null hypothesis for Extroversion cannot be rejected. The fact that F=3.19 is much larger than 1 and p<0.05 indicates that the null hypothesis for Maturity can be rejected. The fact that F=3.62 is much larger than 1 and p<0.05 indicates that the null hypothesis for Self-Confidence can be rejected.

An​ F-curve has df=(15,7).

The number of degrees of freedom for the numerator is 15 The number of degrees of freedom for the denominator is 77.

A​ chi-square independence test is to be conducted to decide whether an association exists between two variables of a population. One variable has two possible values and the other variable has four. What is the degrees of freedom for the χ2-statistic​?

The number of degrees of freedom for the χ2-statistic is 3.

What happens to the power of a hypothesis test if the sample size is increased without changing the significance​ level?

The power of the test increases because the standard deviation of the sampling distribution of the mean decreases. That means that the null hypothesis is rejected for smaller differences between the sample mean and the actual mean.

Define the phrase independent samples.

The sample selected from one of the populations has no effect or bearing on the sample selected from the other population

It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each​ night, on average. After randomly sampling a number of college​ students, the researcher calculated a sample mean of 7.95 hours and obtained a​ p-value of 0.0001 from a​ one-sample t-test. Why is the​ p-value so small when the difference between the sample mean and the hypothesized value of the population mean is only 0.05 hours​ (3 minutes)?

The sample size was very large.

Researchers can make the results statistically significant by increasing the sample size even if the difference between the sample mean and hypothesized value of the population mean is very small.

The statement is true.

In a​ two-way ANOVA, if there is an interaction between Factor A and Factor​ B, then there must be a main effect due to at least one of the factors.

The statement is false. It is possible to have an interaction between the two factors without a main effect due to one of the factors

In a​ two-way ANOVA, if there is no Factor A main effect and no Factor B main​ effect, then there can be no interaction effect between Factor A and Factor B.

The statement is false. It is possible to have no Factor A main effect and no Factor B main​ effect, but have an interaction effect.

The value obtained for the test​ statistic, z, in a​ one-mean z-test is given. Whether the test is two​ tailed, left​ tailed, or right tailed is also specified. For parts​ (a) and​ (b), determine the​ P-value and decide​ whether, at the 5​% significance​ level, the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

The test statistic in a two-tailed test is z=−1.08. The​ P-value is 0.280 ​(Round to three decimal places as​ needed.) At the 5​% significance​ level, the data does not provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis because the obtained​ P-value is greater than the significance level. b. The test statistic in a two-tailed test is z=0.54. The​ P-value is . 589 ​(Round to three decimal places as​ needed.) At the 5​% significance​ level, the data does not provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis because the obtained​ P-value is greater than the significance level.

The value of a statistic used to estimate a parameter is called

The value of a statistic used to estimate a parameter is called​ a(n) point estimate (mean) of the parameter.

The American Association of University Professors​ (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. Independent simple random samples of 35 faculty members in private institutions and 30 faculty members in public institutions yielded the annual​ salaries, in thousands of​ dollars, displayed in Data set 1. At the​ 5% significance​ level, do the data provide sufficient evidence to conclude that mean salaries for faculty in private and public institutions​ differ? Apply the pooled​ t-test.

The value of the​ p-value is 0.01960.0196. Since the ​p-valueless than or equals≤α​, we reject Upper H 0reject H0 and determine that there is sufficient evidence to conclude that mean salaries for faculty in private and public institutions differ.

An advertisement for a diet program described a study performed on 70 obese adults. Each person in the study was weighed before beginning the diet and then 5 weeks after starting the diet. The difference was recorded-a positive value indicates a person lost weight on the diet while a negative value indicates the person gained weight while on the diet. The advertisement gave a​ 95% confidence interval for the average weight change while on the​ diet: ​(−​1,5) lbs. The advertisement says that this shows the diet works at reducing weight for obese adults since more people lost weight than gained weight. What conclusion can be made about the weight loss​ program?

Their interpretation of the confidence interval is not correct. Because 0 is in the​ interval, there is no evidence to indicate that the average weight loss is more than 0 for obese adults.

Consider a 5×7 ANOVA.

There are 5 levels for factor A. There are 7 levels for factor B. cAltogether, there are 35 treatments.

Which of the following is a correct report of a​ two-sample t-test​ (alpha =​ .05) in which the null hypothesis was RETAINED​ (not rejected)?

There's not enough evidence to suggest that Groups A and B differed on Outcome​ X, t(32)​ = 1.82, p​ > .05.

The​ "treatment groups" or​ "model" source of variation in the Analysis of Variance table can also be thought of as​ ________ variation while the​ "error" of​ "residual" source of variation in the Analysis of Variance table can also be thought of as​ ________ variation.

The​ "treatment groups" or​ "model" source of variation in the Analysis of Variance table can also be thought of as between group mean variation while the​ "error" of​ "residual" source of variation in the Analysis of Variance table can also be thought of as within group variation.

Brenda is a huge sports fan. She wondered if there was a relationship between​ someone's favorite sport and where they lived. She randomly sampled 500 American sports fans and asked each what their favorite sport was​ (football, baseball,​ basketball, soccer, or​ other) and what part of the country they lived in​ (Northeast, Southeast,​ Midwest, Rocky​ Mountains, Pacific​ Coast). Assuming all conditions are​ satisfied, which of the following tests should Brenda use to test her​ hypothesis?

The​ chi-square test of independence There was one population and Brett was gathering information on two categorical variables on each person in the sample.

Brenda is a huge sports fan. She hypothesized half of sports fans liked football the​ best, one-quarter liked baseball the​ best, 15% liked basketball the​ best, and​ 5% liked soccer the​ best, and the rest liked some other sport the best. She surveyed 100 sports fans and asked what sport they liked the best. Assuming all conditions are​ satisfied, which of the following tests should Brenda use to test her​ hypothesis?

The​ goodness-of-fit chi-square test There is only one population​ (sports fans) and a categorical variable was examined on this population.

It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each​ night, on average. The researcher randomly sampled 20 college students and found no evidence to reject the null hypothesis at the​ 5% significance level. What is true regarding the​ p-value from this hypothesis​ test?

The​ p-value must have been greater than 0.05.

Suppose increasing the sample size will not change the sample mean or the standard deviation. What will happen to the​ p-value by increasing the sample​ size?

The​ p-value will decrease.

It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each​ night, on average. The researcher randomly sampled 20 college students and obtained a​ p-value of 0.10. Suppose the researcher sampled more college students and that the sample mean and sample standard deviation stayed the same. Would the​ p-value be​ lower, be​ higher, or stay the​ same?

The​ p-value would be lower compared to the​ p-value from the sample with 20 college students.

A study was conducted based on a sample size of 30 individuals. The​ p-value was 0.10. Suppose a researcher conducted another study by taking a random sample of 50 individuals from the same population. Suppose they obtained the same sample mean as in the first study with a sample size of 30.​ (Also assume the population standard deviation is the same for both​ studies.) Which of the following is​ true?

The​ p-value would be smaller for the second study.

H0​: μ1 = μ2 Ha​: μ1 ≠ μ2

This hypothesis test is two-tailed.

Workers at a grocery store undergo shelf-stocking efficiency training. The store supervisor's satisfactions with shelf stocking on the day of the training and three months after the training are compared. Choose the correct answer

This scenario should be analyzed using paired data because the groups are dependent and have a natural pairing.

30 male and 30 female students in a program at school take a class. Their grades are compared.

This scenario should not be analyzed using paired data because the groups are independent and do not have a natural pairing.

A​ p-value is the probability of accepting the null hypothesis.

This statement is false. We never accept the null hypothesis no matter what the​ p-value is. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is true.

Using a more extreme significance level​ (for example, 0.01 instead of​ 0.05)

Using a more extreme significance level decreases power.

Using a​ two-tailed test instead of a​ one-tailed test

Using a​ two-tailed test instead of a​ one-tailed test decreases power.

If there is no seasonal effect on human​ births, one would expect equal numbers of children to be born in each season​ (winter, spring,​ summer, and​ fall). A student takes a census of her statistics class and finds that of the 120 students in the​ class, 26 were born in​ winter, 36 in​ spring, 31 in​ summer, and 27 in fall. She wonders if the excess in the spring is an indication that births are not uniform throughout the year

What is the expected number of births in each season if there is no​ "seasonal effect" on​ births? One should expect 30 births in​ winter, 30 in​ spring, 30 in​ summer, and 30 in fall. chi sq=2.07 ​ How many degrees of freedom does the χ2​-statistic ​have? 3

In a​ chi-square test, when would the null hypothesis be​ true?

When all observed counts are the same as their expected counts

When will a​ chi-square statistic be​ 0?

When all observed counts are the same as their expected counts The numerator of the​ chi-square statistic is ∑over all cells(observed−expected)2. The​ chi-square statistic will be 0 if the numerator is 0 and the only way the numerator will be 0 is if all expected counts are the same as their observed counts.

When doing a multiple comparison method by performing​ two-sample t-tests comparing two group means at a​ time, the significance level on​ ________ two-sample​ t-test is​ ________ to keep the probability of making​ ________ ________ at some predetermined significance level.

When doing a multiple comparison method by performing​ two-sample t-tests comparing two group means at a​ time, the significance level on each two-sample t-test is reduced to keep the probability of making at least one Type I error at some predetermined significance level.

When are conclusions said to be​ "statistically significant"?

When the​ p-value is less than a given significance level

Researchers determine whether​ they'll conduct independent or dependent samples tests​ ______________ collecting their data.

before

If they suspect their data will be highly correlated when using paired​ data, it's recommended that they use​ a(n) _____________ design because this​ _______________ variability and​ _____________ power.

dependent; decreases; increases

Suppose that a​ one-way ANOVA is being performed to compare the means of four populations and that the sample sizes are 17, 16, 16, and 11. Determine the degrees of freedom for the​ F-statistic.

df=(3, 56)

If two variables are positively linearly​ correlated, one of the variables tends to increase as the other

increases

Do people walk faster in an airport when they are departing​ (getting on a​ plane) or after they have arrived​ (getting off a​ plane)? An interested passenger watched a random sample of people departing and a random sample of people arriving and measured the walking speed​ (in feet per​ minute) of each. Which of the following tests is the most appropriate to use to determine if the mean walking speed is different between departing and arriving passengers at an airport​ (assuming all conditions for inference are​ satisfied)?

independent samples​ t-test

In a television​ advertisement, a company called​ "Waist Away" claimed the workout program on their set of DVDs would help people lose weight more than any other DVD workout program. To test this​ claim, an independent​ company, called​ "Slim Down," selected one other DVD program. Then they randomly assigned half the volunteers to the Waist Away program and the other half to the Slim Down program. Each participant was weighed before they started the program and then regularly participated in their assigned program for one month. After one​ month, each participant was weighed again. The amount of weight lost was recorded for each​ person, where negative values indicated a weight gain. The average weight loss of the 20 volunteers on the Waist Away program was 3.1 pounds with a standard deviation of 4​ pounds, while the average weight loss for the 21 volunteers on the Slim Down program was 2.2 pounds with a standard deviation of 2.3 pounds. Which of the following tests is most appropriate to use to determine if the​ company's claim is​ valid?

independent samples​ t-test

2x4 ANOVA. The null hpothesis and research conlcusion for the​ 2-group variable are most like​ a/n:

independent t

Is it a good idea to listen to music when studying for a​ test? A study was performed in which students were randomly assigned to either listen to Mozart or no music while attempting to memorize objects pictured on a page. They were then asked to list all the objects they could remember. Which of the following tests is the most appropriate to use to determine if there is a difference in the mean number of objects remembered between those who listen to Mozart and those who listened to no music while attempting to memorize objects pictured on a page​ (assuming all conditions for inference are​ satisfied)?

independent​ t-test A​ two-sample t-test is appropriate when the variable of interest is​ quantitative, there are two populations​ (or two groups being​ compared), and the population standard deviations are not known.

If two variables are linearly​ correlated, one of the variables tends to decrease as the other increases.

negatively

2x4 ANOVA. The null hpothesis and research conlcusion for the​ 4-group variable are just like​ a/n:

oneway ANOVA

A researcher examined whether four state public schools in a particular state differed on average GRE score.

oneway ANOVA

Many people believe that students gain weight as freshmen in college. To determine if this is​ true, a student randomly sampled 100 freshmen. Each was weighed when college started in the fall and again when they left for home after the spring term. Should a paired​ t-test or a​ two-sample t-test be used to determine if students weigh more at the end of their freshman year compared to the beginning of their freshman​ year, on​ average?

paired​ t-test

Some students do homework with the TV on. Researchers wanted to see if people can work as effectively with distractions as without them. From a group of student​ volunteers, researchers randomly assigned half to do a relatively easy crossword puzzle in a quiet room and the other half to do the same crossword puzzle in a room in which a TV was on. Then each volunteer was to do a different relatively easy crossword puzzle under the other condition. Students were timed on how long it took to complete the puzzle and the difference in each​ student's quiet-room time and​ TV-room time was recorded. Which test is appropriate to use to determine if students take longer to complete the puzzle in the TV room compared to the quiet​ room, on​ average?

paired​ t-test

In​ 1993, the British Medical Journal published an article​ titled, "Is Friday the 13th Bad for Your​ Health?" Researchers in Britain examined how Friday the 13th affects human behavior. One question was whether people tend to stay at home more on Friday the 13th. The accompanying data give the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays​ (the 6th and​ 13th) for five different time periods. Assuming all conditions for inference are​ met, which test is appropriate to use to answer the​ researcher's question of​ interest?

paired​ t-test Since the consecutive Fridays are naturally​ paired, the paired​ t-test is appropriate to use.

The​ F-statistic in a​ one-way Analysis of Variance problem has how many numerator degrees of​ freedom?

the number of groups being compared minus 1

The​ F-statistic in a​ one-way Analysis of Variance problem has how many denominator degrees of​ freedom?

the total sample size of all groups combined minus the number of groups being compared

A hospital administrator wondered whether duration of a particular illness was predicted by treatment location​ (inpatient or​ outpatient) and treatment type​ (A, B,​ C).

twoway ANOVA

If ρ=​0, then the two variables under consideration are linearly

uncorrelated.

The following question pertains to the anxiety scores for each of the three groups shown​ below: Treatment​ A: 1,​ 5, 3 Treatment​ B: 5,​ 3, 7 Treatment​ C: 10,​ 8, 12

​F(2,6) =​ 9.75, MSE​ = 4.00, p​ < .05

Suppose​ that, in a hypothesis​ test, the null hypothesis is in fact false

​No, it is not possible. A Type I error is rejecting the null hypothesis when it is in fact true. ​Yes, it is possible. A Type II error is not rejecting the null hypothesis when it is in fact false.

A student at a large university was interested in how students and faculty felt about the behavior of calling an instructor by their first name. She randomly selected 100 students and 75 faculty and asked each to rate the behavior of calling an instructor by their first name on a scale from 1 to​ 5, where 1=totally inappropriate and 5=totally appropriate. Call each​ individual's rating of this behavior the perception score. A​ 95% confidence interval for the difference in average perception scores between students and faculty ​(students−​faculty) was found to be​ (0.51,1.07). Is there evidence to indicate the average perception score of calling an instructor by their first name is different for students than for​ faculty?

​Yes, since the hypothesized value for the difference in population means of 0 is not between the bounds of the confidence interval at the​ 5% significance level. The null hypothesis in a hypothesis test comparing two means is that the difference between the means is​ 0; that​ is, there is no difference between the means. Since 0 is less than the lower​ bound, it is not one of the possible values the difference in population means could be.​ Therefore, it can be said that there is a difference in the average perception score of calling an instructor by their first name between students and faculty at this large university.

A study was performed on teacher perceptions of the behavior of elementary school children. Teachers rated the aggressive behavior of a sample of 1450 New York City public school children by responding to the​ statement, "This child threatens or bullies others in order to get​ his/her own​ way." Responses were measured on a scale ranging from 1​ (never) to 5​ (always). The summary statistics were x=2.15 and s=1.05. Researchers wanted to test H0​: μx=3 versus HA​: μx≠3. Which of the following tests is the most appropriate to use​ (assuming all conditions for inference are​ satisfied)?

​one-sample t-test A​ one-sample t-test is appropriate when the variable of interest is​ quantitative, there is one​ population, and the population standard deviation is not known.

Are women getting​ taller? A researcher claims that the average height of a woman aged 20 years or older is greater than the 1994 mean height of 63.7 inches. She obtains a random sample of 45 women aged 20 years or older and finds the sample mean to be 63.9 inches. Assume the population standard deviation is 3.5 inches. Which of the following tests is the most appropriate to use to test the​ researcher's claim​ (assuming all conditions for inference are​ satisfied)?

​one-sample z-test A​ one-sample z-test is appropriate when the variable of interest is​ quantitative, there is one​ population, and the population standard deviation is known or assumed to be known.

To study the effect of one factor on the mean of a response variable

​one-way ANOVA

To study the effect of two factors on the mean of a response variable

​two-way ANOVA