Statistics (Chapters 6.3, 6.4, 6.5, 7, 8, 9, 12, and 14) knowledge check

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution? It is almost perfectly symmetrical like the normal distribution. It is flatter and more spread out than the normal distribution. It is taller and narrower than the normal distribution. There is no consistent relationship between the t distribution and the normal distribution.

It is flatter and more spread out than the normal distribution.

By selecting a smaller alpha level, it _____. decreases the likelihood that H0 is rejected. becomes easier to detect a treatment effect. increases the risk of a Type I error. decreases the likelihood that H0 fails to be rejected.

decreases the likelihood that H0 is rejected.

An analysis of variance produces SSbetween = 40 and MSbetween = 20. In this analysis, how many treatment conditions are being compared? k = 2 k = 3 k = 4 k = 2

k = 3

The results of a hypothesis test are reported as follows in a scientific report: t(15) = 2.70, p < .05. Based on this report, how many individuals were in the sample? n = 14 n = 15 n = 16 n = 5

n = 16

A researcher conducts a hypothesis test using a sample from an unknown population. If df = 30 for the t statistic and M = 46 and s2 = 10, how many individuals were in the sample? n = 29 n = 11 n = 31 n = 9

n = 31

A sample of n = 16 scores produces a t statistic of t = +2.00. If the sample is used to measure effect size with r2, which value will be obtained for r2? r2 = 0.10 r2 = 0.20 r2 = 0.11 A sample of n = 16 scores produces a t statistic of t = +2.00. If the sample is used to measure effect size with r2, which value will be obtained for r2? r2 = 0.10 r2 = 0.20 r2 = 0.11 r2 = 0.21

r2 = 0.21

A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores. The hypothesis test produces a z-score of z = +2.27. If the researcher is using a one-tailed test, which is the correct statistical decision? reject the null hypothesis with α = .05 but not with α = .01 reject the null hypothesis with either α = .05 or α = .01 fail to reject the null hypothesis with either α = .05 or α = .01 fail to reject the null hypothesis with α = .05 but not with α = .01

reject the null hypothesis with α = .05 but not with α = .01

A sample of n = 7 scores has a mean of M = 65 and an estimated standard error of 2 points. What is the sample variance? s2 = 24 s2 = 36 s2 = 28 s2 = 14

s2 = 28

Which of the following results from a hypothesis test involving the computation of a t-statistic is structured correctly based on standards for presenting hypothesis tests in scientific reports? t(19) = 2.30, r2 = 0.42, p < .05 t(19) = 2.30, p < .05, r2 = 0.42 r2 = 0.42, t(19) = 2.30 , p < .05 t = 2.30, df = 19, p < .05, r2 = 0.4

t(19) = 2.30, p < .05, r2 = 0.42

A vertical line drawn through a normal distribution at z = +2.11 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the tail? 0.6915 0.4826 0.9826 0.0174

0.0174

Suppose the correlation between height and weight for adults is r = +0.40. What proportion (or percent) of the variability in weight can be explained by its relationship with height? 40% 60% 16% 84%

16%

For the linear equation Y = 2X + 4, if X increases by 1 point, by how much will Y increase? 1 point 2 points 3 points 4 poin

2 points

If random samples, each with n = 16 scores, are selected from a normal population with µ = 100 and σ = 20, how much difference, on average, should there be between a sample mean and the population mean? 16 points 3 points 4 points 5 points

5 points

A set of n = 25 pairs of scores (X and Y values) in a research study has a Pearson correlation of r = 0.80. What percentage of the variance for the Y scores is predicted by its relationship with X? 36% 20% 80% 64%

64%

For an ANOVA comparing three treatment conditions, what is stated by the alternative hypothesis (H1)? There are no differences between any of the population means. At least one of the three population means is different from another population mean. All three of the population means are different from each other. One population mean is different from one of the other population means, but not the other population mean.

At least one of the three population means is different from another population mean.

A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, which is the probability that the score will be less than X = 78? A-p = 0.3643 B-p = 0.1765 C-p = 0.8643 D -p = 0.1357

D -p = 0.1357

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments and obtains t(12) = 4.00. If the researcher had used an ANOVA to evaluate the data, what F-ratio would be obtained? F(1, 12) = 2.00 F(1, 12) = 16.00 F(1, 11) = 2.00 F(1, 11) = 16.00

F(1, 12) = 16.00

An independent-measures research study compares three treatment conditions using a sample of n = 5 in each condition. For this study, the three samples have SS1 = 10, SS2 = 20, and SS3 = 15. Which value would be obtained for MSwithin? MSwithin = 3.21 MSwithin = 3.75 MSwithin = 5.00 MSwithin = 3.33

MSwithin = 3.75

An independent-measures experiment with three treatment conditions has a sample of n = 10 scores in each condition. If all three conditions have the same total, T1 = T2 = T3, what is SSbetween? SSbetween = 0 SSbetween = 1.00 SSbetween = 10 This cannot be determined based on the information provided.

SSbetween = 0

Which statement below is consistent conceptually with what a computed Pearson's r value represents? The Pearson's r value represents the degree to which X and Y scores vary separately relative to how much X and Y scores covary together. The Pearson's r value represents the degree to which X and Y scores covary together relative to how much X and Y scores vary separately. The Pearson's r value represents the degree to which between groups variability exists, relative to within groups variability. The Pearson's r value represents the degree to which within groups variability exists, relative to between groups variability

The Pearson's r value represents the degree to which X and Y scores covary together relative to how much X and Y scores vary separately.

Assuming all other factors are held constant, if the df value for a two-tailed t test with α = .05 were increased from df = 6 to df = 20, what would happen to the critical values for t? The critical values would further from t = 0. The critical values would move closer to t = 0. The critical values would not change. This is impossible to determine without more information.

The critical values would move closer to t = 0.

A sample of n = 25 scores produces a t statistic of t = +2.052. If the researcher is conducting a two-tailed hypothesis test, which of the following is the correct statistical decision? The researcher should reject the null hypothesis with α = .05 but not with α = .01. The researcher should reject the null hypothesis with either α = .05 or α = .01. The researcher should fail to reject the null hypothesis with either α = .05 or α = .01. This is impossible to determine based on the provided information.

The researcher should fail to reject the null hypothesis with either α = .05 or α = .01.

A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z = +2.37. If the researcher is using a two-tailed test, which decision should be made? The researcher should reject the null hypothesis with α = .05 but not with α = .01. The researcher should reject the null hypothesis with either α = .05 or α = .01. The researcher should fail to reject H0 with either α = .05 or α = .01. The researcher should fail to reject the null hypothesis with α = .01 but not with α =

The researcher should reject the null hypothesis with α = .05 but not with α = .01.

Which of the following statements correctly describes the effect of increasing the alpha level (for example, from a = .01 to a = .05)? This action increases the likelihood of rejecting H0 and increases the risk of a Type I error. This action decreases the likelihood of rejecting H0 and increases the risk of a Type I error. This action increases the likelihood of rejecting H0 and increases the risk of a Type II error. This action decreases the likelihood of rejecting H0 and increases the risk of a Type II error.

This action increases the likelihood of rejecting H0 and increases the risk of a Type I error.

The critical boundaries for a hypothesis test are z = +1.96 and z = -1.96. If the z-score for the sample data is z = -1.90, which is the correct statistical decision? fail to reject H1 fail to reject H0 reject H1 reject H0

fail to reject H0

A sample is selected from a normal population with µ = 40 σ = 10. If the sample mean of M = 46 produces a z-score of z = +3.00, then how many scores are in the sample? n = 25 n = 4 n = 9 n = 36

n = 25

Consider a normal population with µ = 75 and σ = 10. A sample of at least which size needs term-35to be obtained in order to achieve a standard error of σM = 2.00 or less? n = 36 n = 16 n = 25 n = 4

n = 25

A sample of n = 4 scores is selected from a normal population with a mean of µ = 50 and a standard deviation of σ = 20. What is the probability of obtaining a sample mean less than M = 52? p = 0.6915 p = 0.3085 p = 0.5793 p = 0.5602

p = 0.5793

A normal distribution has µ = 20 and σ = 4. Which is the probability of randomly selecting a score greater than X = 25 from this distribution? p = 0.3944 p = 0.1056 p = 0.8944 p = 0.7888

p = 0.8944

A random sample of n = 16 scores is selected from a normal distribution with µ = 500 and σ = 200. For this sample, which of the following statements is true? p(402 < M < 598) = 0.95 p(425 < M < 575) = 0.95 p(450 < M < 550) = 0.95 p(490 < M < 510) = 0.95

p(402 < M < 598) = 0.95

Which of the following is an accurate definition of a Type I error? rejecting a false null hypothesis rejecting a true null hypothesis failing to reject a false null hypothesis failing to reject a true null hypothesis

rejecting a true null hypothesis

Consider a researcher who is conducting final clinical trials to validate that a new treatment for anxiety is effective. This researcher is extremely focused on avoiding mistakes in concluding that this new treatment is effective when it really is not when conducting their research. What should this researcher do? set a low sample mean set a high sample mean set a low alpha level set a high alpha level

set a low alpha level

What is measured by the numerator of the z-score test statistic? the likely distance between M and µ that would be expected if H0 was false the distance between the sample mean and hypothesized population mean the position of the sample mean relative to the critical region the boundaries for the critical region(s)

the distance between the sample mean and hypothesized population mean

Larry wants to do everything possible to be in a position to detect that a treatment he has designed is effective given that it is actually effective. Which of the following should he do? decrease the sample size use an alpha (α) of .01 instead of .05 decrease the population standard deviation use an alpha (α) of .05 instead of .01

use an alpha (α) of .05 instead of .01

At an organization, scoring in the middle 80% of employees regarding job performance is designated as satisfactory. Job performance is a normally distributed variable. Individuals designated as having satisfactory job performance would have job performance scores that correspond with z-scores equal to or between _____. z = -1.49 and z = +1.49 z = -0.39 and z = +0.39 z = -0.85 and z = +0.85 z = -1.28 and z = +1.28

z = -1.28 and z = +1.28

A sample of n = 7 scores is selected from a population with an unknown mean (µ). The sample has a mean of M = 40 and a variance of s2 = 63. Which of the following is the correct 95% confidence interval for µ? µ = 40 ± 7.341 µ = 40 ± 22.023 µ = 40 ± 7.095 µ = 40 ± 21.285

µ = 40 ± 7.341