Ch.9 stats

A sample of n = 25 scores has a mean of M = 40 and a variance of s2 = 100. What is the estimated standard error for the sample mean?​

2

Which of the following describes the function of a confidence interval?​

​It uses a sample mean to estimate the corresponding population mean.

For a sample of n=16 scores with SS=375 compute the sample variance and the estimated standard error for the sample mean

S2=25 Sm=1.25

Which set of characteristics will produce the smallest value for the estimated standard error?​

A large sample size and a small sample variance

If exactly 5% of the t distribution is located in the tail beyond t=2.353, how many degrees of freedom are there?

3

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?

0.09 medium effect

Assuming all other factors stay the same, what happens to the portion of the data in both hills as the degrees of freedom increases with a T-statistic?

The proportion in the two tails combined decreases

A hypothesis test with a sample of n = 25 participants produces a t statistic of t = +2.53. Assuming a one-tailed test with the critical region in the right-hand tail, what is the correct decision?​

The researcher can reject the null hypothesis with either α = .05 or α = .01.

A sample of n = 25 scores produces a t statistic of t = 2.062. If the researcher is using a two-tailed test, then which of the following is the correct statistical decision?​

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

Which of the following is not an assumption of hypothesis testing using a t-statistic?

The sample size must be greater than 30

Which of the following is a fundamental difference between the t statistic and a z-score?​

The t statistic uses the sample variance in place of the population variance.

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?

d=1 large effect

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?

t = 2.55, yes

If other factors are held constant, how does sample size influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?​

​A larger sample increases the likelihood but has little influence on measures of effect size.

A sample has a mean of M = 39.5 and a standard deviation of s = 4.3, and produces a t statistic of t = 2.14. For a two-tailed hypothesis test with α = .05, what is the correct statistical decision for this sample?​

​It is impossible to make a decision about H0 without more information.

If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that m = 80?​

​M = 85 and large sample variance

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?

36

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?

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

Check My Work 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 one-tailed t statistic

Which value is not included in the calculation of an estimated Cohen's d?

n

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

When n is especially small, the T distribution is______and______

Flatter, and more spread out

Which of the following is a problem with using the Z score statistic?

It requires knowing the population variance, which is often difficult to obtain

How does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's

Larger variance increases both the likelihood and measures of effect size.

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.

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

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?

u > 103 (underlined)