Stats FINAL

Which of the following is the correct null hypothesis for an independent-measures t test? a. μ1 - μ2 = 0 b. M1 - M2 = 0 c. μ1 - μ2 =/= 0 d. M1 - M2 =/= 0

a. μ1 - μ2 = 0

T or F: . You are more likely to make a Type I error with a sample of n = 4,000 than with a sample of n = 100,000,000 even if you use α = .05 for both tests.

False

True or False: Distributions of sample means (sampling distributions) are normal when they are based on samples of at least n = 30.

False

True or False: It is impossible for fewer than half of the scores in a distribution to have values greater than the mean

False

True or False: In general, the larger the value of the estimated standard error, the lower the likelihood of rejecting the null hypothesis

True

True or False: Statistical power plus the likelihood of a Type II error always equals 1.0.

True

True or False: Within any normal or symmetrical distribution of scores, the location specified by z = +.1 and the location specified by z = -.1 are exactly the same distance from the mean.

True

A population of scores has μ = 50 and σ= 12. If you subtract 1 point from every score in the population, then the new standard deviation will be____. a. Insufficient information, cannot be determined b. 11 c. 12 d. 13

c. 12

An analysis of variance produces SSbetween = 30, SSwithin = 60, and an F-ratio with df = 2, 15. For this analysis, what is the F-ratio? a. 30/60 = 0.50 b. 60/30 = 2.00 c. 15/4 = 3.75 d. 4/15 = 0.27

c. 15/4 = 3.75

For the AxB summation equation, assume that factor A has 3 levels and factor B has 5 levels. After calculating the squared result for i=2, and j=5, what is the value for i for the next (upcoming) iteration? a. 1 b. 2 c. 3 d. 5

c. 3

For a normal distribution with = 500 and σ = 100, what is the minimum score necessary to be in the top 90% of the distribution? a. 628 b. 572 c. 372 d. 472

c. 372

Which of the following will increase the power of a statistical test? a. Change α from .05 to .01. b. Change from a one-tailed test to a two-tailed test. c. Change the sample size from n = 25 to n = 100. d. None of the options will increase power.

c. Change the sample size from n = 25 to n = 100.

A sample of n = 25 scores is determined to have a standard error of 4 points. What is the standard deviation for the population from which the sample was obtained? a. 50 b. 10 c. 2/5 d. 20

d. 20

True or False:A score with a value higher than the mean will have a negative z-score

False

What proportion of a normal distribution falls between z = -1.96 and z = +1.96? a. 0.7540 b. 0.9500 c. 0.7580 d. 0.2420

b. 0.9500

Describe the 95% confidence interval of the population proportion with a sample proportion of .5, and a sample size of 25? a. .5 ± 2.0 b. It's a good-hearted fellow, with malice toward none c. .5 ±.196 d. The true population proportion is between .4 and .6

c. .5 ±.196

True or False: As sample size decreases, the estimated standard error increases.

True

T or F: For a hypothesis test using a t statistic, the boundaries for the critical region will change if the sample size is changed

True

T or F: an increase in the sample variance makes it less likely that the t statistic will be large enough to reject the null hypothesis

True

True or False: As df increases,the student's t distribution approaches a normal distribution

True

For any normal distribution, what are the z-score values that form the boundaries for the middle 74%? a. z = +/- 1.13 b. z = +/- 0.84 c. z = +/- 0.52 d. z = +/- 1.96

a. z = +/- 1.13

Assuming that the null hypothesis is true, what is the probability of obtaining a sample that generates a z-value at least as extreme as z = -1.19? a. .234 b. .117 c. .8830 d. 1.766

a. .234

What is the probability of getting at least 12 questions correct by blindly guessing on a 40-item exam, in which each item contains four possibilities? a. .2912 b. .7088 c. .4176 d. .2643

a. .2912

A test statistic of z = -2.88 was calculated. Estimate the p-value a. .4% b. 2% c. .2% d. 1.90%

a. .4%

If a hypothesis test is found to have power = 0.70, then what is the probability that the test will result in a Type II error? a. 0.30 b. 0.70 c. p > 0.70 d. Cannot be determined without more information

a. 0.30

For the AxB summation equation, assume that factor A has 3 levels and factor B has 5 levels. After calculating the squared result for i=1, and j=4, what is the value for i for the next (upcoming) iteration? a. 1 b. 2 c. 3 d. 5

a. 1

On a 40-item exam, in which each item contains four possibilities, you get 16 correct. You test the 2-tailed null hypothesis which claims that the likelihood of getting an item correct is .25. What is z-calc? a. 2.22 b. 2.04 c. 2.05 d. 1.88

a. 2.22

For an independent-measures ANOVA comparing three treatments with a sample of n = 5 in each treatment, what is the critical value for the F-ratio using α = .05? a. 3.88 b. 3.49 c. 3.74 d. 3.34

a. 3.88

Which of the following confidence intervals also indicates a significant difference between treatments with α = .05? a. Estimate that μ1 - μ2 is in an interval between 2 and 10 with 90% confidence. b. Estimate that μ1 - μ2 is in an interval between -2 and 8 with 90% confidence. c. Estimate that μ1 - μ2 is in an interval between 2 and 10 with 95% confidence. d. Estimate that μ1 - μ2 is in an interval between -2 and 8 with 95% confidence

a. Estimate that μ1 - μ2 is in an interval between 2 and 10 with 90% confidence

What happens to the critical value for a chi-square test if the number of categories is increased? a. The critical value also increases. b. The critical value decreases. c. The critical value depends on the sample size, not the number of categories. d. The critical value is determined entirely by the alpha

a. The critical value also increases.

What is stated by the null hypothesis (H0) for an ANOVA? a. There are no differences between any of the population means. b. At least one of the population means is different from another mean. c. All of the population means are different from each other. d. None of the other 3 choices is correct (34)

a. There are no differences between any of the population means.

In general, decreasing the alpha level (for example, from .05 to .01) will ________. a. decrease the likelihood of rejecting H0 and decrease the risk of a Type I error b. increase the likelihood of rejecting H0 and decrease the risk of a Type I error c. decrease the likelihood of rejecting H0 and increase the risk of a Type I error. d. increase the likelihood of rejecting H0 and increase the risk of a Type I error.

a. decrease the likelihood of rejecting H0 and decrease the risk of a Type I error

In general, increasing the sample size (for example, from n = 4 to n = 50) will ________ the risk of Type-I error (assuming α is held constant at .05). a. have no influence on b. decrease c. increase d. do something to

a. have no influence on

For a fixed level of significance, the critical value for chi-square will ______. a. increase as the df value increases. b. decrease as the df value increases. c. increase as the sample size increases. d. decrease as the sample size increases.

a. increase as the df value increases.

For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples? a. increase the likelihood of rejecting H0 and increase measures of effect size b. increase the likelihood of rejecting H0 and decrease measures of effect size c. increase the likelihood of rejecting H0 and have little or no effect on measures of effect size d. decrease the likelihood of rejecting H0 and have little or no effect on measures of effect size

a. increase the likelihood of rejecting H0 and increase measures of effect size

If the mean and variance are computed for each sample in an independent-measures two-factor experiment, then which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA? a. large differences between sample means and small sample variances b. large differences between sample means and large sample variances c. small differences between sample means and small sample variances d. small differences between sample means and large sample var

a. large differences between sample means and small sample variances

The z-score boundaries for the critical regions in a hypothesis test are determined by ________. a. the alpha level b. the size of the standard error c. the sample data d. the null hypothesis

a. the alpha level

In a 2-factor ANOVA with 2 levels of the A factor, if MA1=5 and MA2=6, what can you conclude if the grand mean is equal to 5.2? a. the two sample sizes are not equal b. there's not enough information to draw a conclusion c. A2 has more scores than A1 d. mistakes were made in the calculation of the grand

a. the two sample sizes are not equal

On a 40-item exam, in which each item contains four possibilities, you get 16 correct. Does this allow you to reject the 2-tailed null hypothesis which claims that the likelihood of getting an item correct is .25? a. yes b. no c. only if the alpha level is p=0.10 d. can't determine without knowing degrees of free

a. yes

if two samples are selected from the same population and are testing the same null hypothesis, under what circumstances will the two samples have exactly the same t statistic? a) none of the other option are correct b) if the samples are the same size, have the same sample mean, and have the same sample variance c) if the samples are the same size and have the same mean d) if the sample size is the same for both samples

b) if the samples are the same size, have the same sample mean, and have the same sample variance

Assuming that the null hypothesis is true, what is the likelihood of obtaining a sample mean as least as extreme as one that produces a z-score of 2.58? a. .99% b. .98% c. .985% d. 1.0%

b. .98%

23. Assuming that the null hypothesis is true, what is the likelihood of obtaining a sample mean as least as extreme as one that produces a t(30) score of -2.58? a. 2% b. Lower than 2%, but greater than 1% c. 5% d. Lower than 4%, but greater than 2%

b. Lower than 2%, but greater than 1%

Using z-scores, a population with μ = 47.79 and σ= 6.002 is standardized so that the new mean is u = 50.902 and a = 1.128. How does an individual's z-score in the new distribution compare with his/her z-score in the original population? a. Cannot be determined with the information given b. New z = old z c. New z = (50.902/1.128)(old z) d. New z = (old z)(1.128) + 50.902

b. New z = old z

If an analysis of variance is used for the following data, what would be the effect of changing the value of SS2 to 100? Sample Data M1 = 15 M2 = 25 SS1 = 90 SS2 = 70 a. increase SSwithin and increase the size of the F-ratio b. increase SSwithin and decrease the size of the F-ratio c. decrease SSwithin and increase the size of the F-ratio d. decrease SSwithin and decrease the size of the F-ratio

b. increase SSwithin and decrease the size of the F-ratio

Two separate samples are being used to estimate the population mean difference between two treatment conditions. Which of the following would produce the widest confidence interval? a. n1 = n2 = 10 with a pooled variance of 10 b. n1 = n2 = 10 with a pooled variance of 100 c. n1 = n2 = 20 with a pooled variance of 10 d. n1 = n2 = 20 with a pooled variance of 100

b. n1 = n2 = 10 with a pooled variance of 100

Which of the following accurately describes the chi-square distribution? a. symmetrical with a mean of zero b. positively skewed with all values greater than or equal to zero c. negatively skewed with all values greater than or equal to zero d. symmetrical with a mean equal to n - 1

b. positively skewed with all values greater than or equal to zero

In the table used to assess the test statistic, what does the vertical line in the right tail of the F distribution indicate when alpha = .05? a. the 90th percentile b. the 95th percentile c. it depends on degrees of freedom d. the 99th percentile

b. the 95th percentile

What value is estimated with a confidence interval using the repeated-measures t statistic? a. the mean for a sample of difference scores b. the mean for a population of difference scores c. the difference between two population means d. the difference between two sample means

b. the mean for a population of difference scores

What does the standard error of the proportion describe? a. the variability of the binomial distribution b. the variability of the distribution of sample proportions c. the amount of variability that distinguishes a binomial from a normal distribution d. The variability of the true parent distribution of the population

b. the variability of the distribution of sample proportions

Which of the following is the correct null hypothesis for a repeated-measures t test? a. MD = 0 b. μD = 0 c. μ1 = μ2 d. M1 = M2

b. μD = 0

Which of the following confidence intervals also indicates a significant two-tailed difference between treatments with α level of .05? a. Estimate that μ1 - μ2 is in an interval between 2 and 10 with 94% confidence. b. Estimate that μ1 - μ2 is in an interval between -2 and 8 with 90% confidence. c. Estimate that μ1 - μ2 is in an interval between 2 and 10 with 99% confidence. d. Estimate that μ1 - μ2 is in an interval between -2 and 8 with 95% confide

c. Estimate that μ1 - μ2 is in an interval between 2 and 10 with 99% confidence.

A test statistic of t(10) = 2.5 was calculated. Estimate the p-value a. Exactly 2.5% b. Lower than 1%, greater than .5% c. Lower than 4%, greater than 2% d. Lower than 2%, greater than 1%

c. Lower than 4%, greater than 2%

What happens to the critical value for a chi-square test if the size of the sample is increased? a. The critical value also increases. b. The critical value decreases. c. The critical value depends on the number of categories, not the sample size. d. The critical value is determined entirely by the alpha l

c. The critical value depends on the number of categories, not the sample size.

A one-tailed, directional test has a critical value (value needed to reject the null hypothesis) of 1.645 (alpha = .05). Based on this information, it is probably safe to assume that: a. This test uses the student's t distribution. b. The sample used to obtain the test statistic was between n=100 and n=1000. c. The population standard deviation is known. d. The population standard deviation is unknown

c. The population standard deviation is known.

Assume that the 95% confidence interval around a sample proportion ranges from .4 to .6. What can we infer? a. The true sample proportion is between .4 and .6 b. The true population proportion is between .4 and .6 c. We can be 95% confident that the population proportion lies in this interval d. We can be 95% confidence that the population proportion is .5

c. We can be 95% confident that the population proportion lies in this interval

In a chi-square test for independence or goodness of fit _____. a. Σfe = n b. Σfe = Σfo c. both Σfe = n and Σfe = Σfo d. neither Σfe = n nor Σfe = Σfo

c. both Σfe = n and Σfe = Σfo

a researcher is predicting that a treatment will decrease scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test is: a) near the middle of the sampling distribution b) divided equally between the two tails of the distribution c) in the left-hand tail of the distribution d) in the right-hand tail of the distribution

c. in the left-hand of the distribution

In general, how are degrees of freedom obtained? a. n-1 b. N-1 c. number of deviations minus one d. it depends on which sum of squares is being calculated

c. number of deviations minus one

Which of the following is an accurate definition for the power of a statistical test? a. the probability of rejecting a true null hypothesis b. the probability of supporting true null hypothesis c. the probability of rejecting a false null hypothesis d. the probability of supporting a false null hypothesis

c. the probability of rejecting a false null hypothesis

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment. If all of the participants show improved performance of 8 or 9 points after treatment, then the researcher should find ______. a. a sample mean difference near zero b. a t statistic near zero c. the variance of the difference scores is near zero d. None of the other options is correct.

c. the variance of the difference scores is near zero

Why do we divide SS by df? a. to obtain an average b. no one knows c. to convert SS into a statistic d. to estimate the sample varian

c. to convert SS into a statistic

A population of scores has μ = 50 and σ = 5. If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation? a. μ = 3000 and σ = 300 b. μ = 150 and σ = 5 c. μ = 150 and σ = 15 d. μ = 53 and σ= 8

c. μ = 150 and σ = 15

With α = .01 and df = 25, the critical value for a one-tailed t test is t = 2.485. Assuming all other factors are held constant, if the df value were decreased, the critical value of t would _______. a) not enough information to answer b) stay the same c) decrease d) increase

d) increase

If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study? a. MD = 5 with s2 = 5 for the difference scores b. MD = 5 with s2 = 10 for the difference scores c. MD = 3 with s2 = 10 for the difference scores d. MD = 3 with s2 = 20 for the difference score

d. MD = 3 with s2 = 20 for the difference score

In a two-tailed z-test, why is ±1.96 important? a. ±1.96 has a p-value of .05. b. ±1.96 has a p-value of .025. c. A test statistic of equal or greater extremity results in rejection of the null hypothesis. d. More than one of the above is correct.

d. More than one of the above is correct. (A and C)

Which of the following is an advantage of transforming X values into z-scores? a. All negative numbers are eliminated. b. All scores are moved closer to the mean. c. The distribution is transformed to a normal distribution. d. None of the other options is an advantage.

d. None of the other options is an advantage.

The value of one score in a distribution is changed from X = 20 to X = 30. Which measure(s) of central tendency is (are) certain to be changed? a. The mode b. The median and the mean c. The median d. The mean

d. The mean

In a two-factor ANOVA, what is the implication of a significant AxB interaction for the main effects? a. At least one of the main effects must also be significant. b. Both of the main effects must also be significant. c. Neither of the two main effects can be significant. d. The significance of the interaction has no implications for the main

d. The significance of the interaction has no implications for the main

If an analysis of variance is used for the following data, what would be the effect of changing the value of M1 to 20? Sample Data M1 = 15 M2 = 25 SS1 = 90 SS2 = 70 a. increase SSbetween and increase the size of the F-ratio b. increase SSbetween and decrease the size of the F-ratio c. decrease SSbetween and increase the size of the F-ratio d. decrease SSbetween and decrease the size of the F-ratio

d. decrease SSbetween and decrease the size of the F-ratio