Chapter 9

The results of a hypothesis test are reported as follows: "t(35) = 1.65, p < .05." Based on this report, how many individuals were in the sample? a. 36 b. 35 c. 34 d. It cannot be determined from the information provided.

36

For a sample size of 9 with SS = 100 and sample mean M = 18.2, what is the probability that the true population mean will be between 16.56 and 19.84? a. 20% b. 50% c. 70% d. 80%

80%

True or false As the degrees of freedom increases, the variance decreases because df is in the denominator. Therefore the estimated standard error decreases. Because sM is in the denominator for the t statistic, this means that the t statistic will increase. If this is true, then the area of the critical region decreases

True

True or False If the population standard deviation is known, a t-score would be used.

False, z-score would be used

A sample is selected from a population with μ = 50, and a treatment is administered to the sample. If the sample variance is s2 = 121, which set of sample characteristics has the greatest likelihood of rejecting the null hypothesis? a. M = 49 for a sample size of n = 15 b. M = 49 for a sample size of n = 75 c. M = 45 for a sample size of n = 15 d. M = 45 for a sample size of n = 75

M = 45 for a sample size of n = 75

A researcher is conducting a directional (one-tailed) test with a sample of n = 10 to evaluate the effect of a treatment that is predicted to increase scores. If the researcher obtains t = 2.770, then what decision should be made? a. The treatment has a significant effect with either α = .05 or α = .01. b. The treatment does not have a significant effect with either α = .05 or α = .01. c. The treatment has a significant effect with α = .05 but not with α = .01. d. The treatment has a significant effect with α = .01 but not with α = .05.

The treatment has a significant effect with α = .05 but not with α = .01.

The t distribution is _______________ with a smaller n. a. flatter and more spread out b. more like the z distribution

flatter and more spread out

When n is especially small, the t distribution is __________ and _______________. a. taller, less spread out b. taller, more spread out c. flatter, less spread out d. flatter, more spread out

flatter, more spread out

√SS = a. s^2 b. s

s^2

r^2 = a. t/t+df b. t^2/t^2+df c. t^2/t^2-df

t^2/t^2+df

s = a. √SS/df b. √SS/n

√SS/df

Which of the following is not an assumption for hypothesis testing using the t statistic? a. The population sampled must be normal. b. The values in the sample must consist of independent observations. c. The sample size must be greater than 30. d. The population standard deviation is unknown.

The sample size must be greater than 30.

True or False The likelihood of rejecting the null hypothesis increases when the sample size increases and the difference between the sample mean and population mean increases.

true

A researcher selects a sample of n = 25 individuals from a population with a mean of μ = 103 and administers a treatment to the sample. If the research predicts that the treatment will decrease scores, then what is the correct statement of the null hypothesis for a directional (one-tailed) test? a. μ ≥ 103 b. μ > 103 c. μ ≤ 103 d. μ < 103

μ ≥ 103

A researcher is looking at the impact that television has on children. Children are placed in a room with a variety of toys and a television playing a cartoon. The researcher predicts that the children will spend more than half of their 30 minutes looking at the television. The researcher tested 15 children and found a sample mean of M = 17 minutes spent watching the television with SS = 79. In order to test this hypothesis, what does the researcher need? a. A one-tailed z-score b. A two-tailed z-score c. A one-tailed t statistic d. A two-tailed t statistic

. A one-tailed t statistic

A scientist is studying the impact of certain vitamins on a person's ability to remember. The sample size for the experimental group was 25. When a two-tailed t test was calculated, the t statistic came out to be 1.54. What are the percent of variance (r2) and the size of the effect? a. 0.06, which indicates a medium effect b. 0.06, which indicates a large effect c. 0.09, which indicates a medium effect d. 0.09, which indicates a small effect

0.09, which indicates a medium effect

A random sample of n = 30 individuals is selected from a population with μ = 15, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 23.1 with SS = 400. In order to determine if the treatment had a significant effect, which of the following can we use? a. A z-score only. There is not enough information to use a t statistic. b. A t statistic. There is not enough information to use a z-score. c. Either a z-score or a t statistic. There is enough information for both. d. Neither a z-score nor a t statistic. There is not enough information to use either.

A t statistic. There is not enough information to use a z-score.

A researcher failed to reject the null hypothesis with a two-tailed test using α = .05. If the researcher had used the same data with a one-tailed test, what can we conclude? a. The researcher would definitely reject the null hypothesis using a one-tailed test. b. The researcher would definitely not reject the null hypothesis using a one-tailed test. c. The researcher would probably reject the null hypothesis using a one-tailed test. d. It is impossible to tell whether or not the researcher would reject the null hypothesis using a one-tailed test.

It is impossible to tell whether or not the researcher would reject the null hypothesis using a one-tailed test.

Which of the following is a problem with using the z-score statistic? a. It requires knowing the population variance (or standard deviation, which is often difficult to obtain. b. It requires very large samples in order to be effective. c. It is too cumbersome to calculate. d. It requires very small standard deviations in order to be effective.

It requires knowing the population variance (or standard deviation, which is often difficult to obtain.

Assuming all other factors stay the same, what happens to the proportion of the data in both tails as the degrees of freedom increases with a t statistic? a. The proportion in the two tails combined increases. b. The proportion in the two tails combined decreases. c. The proportion in the two tails stays the same. d. It is impossible to tell without knowing the estimated standard error.

The proportion in the two tails combined decreases.

True or False Because the researcher is predicting a value with a lower bound ("more than half"), he wants a one-tailed test. Because the population variance (or standard deviation) is unknown, he will need a t statistic.

True

True or False The likelihood of rejecting the null hypothesis increases when the sample size increases and the variance decreases.

True

True or False The t statistic must have a normally distributed population and independent observations. If the population standard deviation is known, a z-score would be used instead. There is no assumption on sample size for the t statistic.

True

A population of trees has a mean leaf length of 6.2 inches. A sample of 17 of these trees in a particular neighborhood has a mean length of 3.2 inches. If SS = 144 for this sample, what is Cohen's d for this example, and what is the strength of the treatment effect, which in this case is growing in a particular neighborhood? a. d = 0.5, which demonstrates a small effect. b. d = 0.5, which demonstrates a medium effect. c. d = 1, which demonstrates a medium effect. d. d = 1, which demonstrates a large effect.

d = 1, which demonstrates a large effect.

A decrease in the obtained difference (M - u) ____________ the t statistic.

decreases

An increase in the sample variance (s^2)___________the t statistic.

decreases

A decrease in the sample standard deviation (s)___________ the t statistic.

increases

An increase in the sample size (n)__________ the t statistic.

increases

d= 0.8 = _______effect size

large

r^2= 0.25 = _______effect size

large

d= 0.5 = _______effect size

medium

r^2= 0.09 = _______effect size

medium

Which value is not included in the calculation of an estimated Cohen's d? a. μ b. n c. M d. s

n

A sample is selected from a population and a treatment is administered to the sample. If there is a 3-point difference between the sample mean and the original population mean, which set of sample characteristics has the greatest likelihood of rejecting the null hypothesis? a. s 2 = 10 for a sample with n = 50 b. s 2 = 4 for a sample with n = 10 c. s 2 = 10 for a sample with n = 10 d. s 2 = 4 for a sample with n = 50

s 2 = 4 for a sample with n = 50

For a sample of n = 16 scores with SS = 375, compute the sample variance and the estimated standard error for the sample mean. a. s2 = 23.44, sM = 1.21 b. s2 = 25, sM = 1.25 c. s2 = 25, sM = 1.5625 d. s2 = 25, sM = 1.29

s2 = 25, sM = 1.25

s^2= SS/n-1 = SS/df a. sample variance b. sample mean

sample variance

d= 0.2 = _______effect size

small

r^2= 0.1 = _______effect size

small

d= 0.2 = _______effect size d= 0.5 = _______effect size d= 0.8 = _______effect size

small medium large

r^2= 0.1 = _______effect size r^2= 0.09 = _______effect size r^2= 0.25 = _______effect size

small medium large

A switch from using a two-tailed test to a one-tailed test__________ the t statistic.

stays the same

To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 31, and the treatment is administered to the individuals in the sample. After a treatment, the sample mean is found to be M = 32.7 with a sample variance of s2 = 4. If the sample size is n = 9, what is the t statistic, and is the data sufficient to conclude that the treatment increased the scores significantly? Use a one-tailed test and α = .01. a. t = 2.55, which is sufficient to reject the null hypothesis b. t = 2.55, which is not sufficient to reject the null hypothesis c. t = 3.355, which is not sufficient to reject the null hypothesis d. t = 3.355, which is sufficient to reject the null hypothesis

t = 2.55, which is not sufficient to reject the null hypothesis

To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 25, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 27.4 with SS = 64. If the sample consists of 9 individuals, what is the t statistic, and are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05? a. t = 2.55, yes b. t = 2.38, no c. t = 2.28, yes d. t = 2.28, no

t = 2.55, yes