2220 Exam 2 Questions

Sample mean (M) = 50 Population mean (µ) = µM = 47 Sample standard deviation (s) = 4 Sample size (N) = 25 Cohen's d?

0.75

Sample mean (M) = 78.6 Population Mean (µ) = 77 Population standard deviation (σ) = 2 Standard error (σM) = 0.4 Sample size (N) = 25 Based on this information, calculate the effect size, Cohen's d. Please provide at least two decimal places when reporting your answer (if relevant).

0.8

When considering z scores of +or- 1.25 from the standard normal distribution, what percentage of the distribution of scores are at least as extreme as those two z scores (i.e., at least that distant from the mean)? Please provide your answer as a percentage with two decimal places. (You do not need to include the percent symbol).

21.12

Consider Z scores of + or - 1.05. What percentage of scores are at least as extreme as + or - 1.05 Z scores?

29.38%

Please calculate the sample standard deviation for the following sample of five numbers: 2, 4, 6, 8, 10 Please provide two decimal places when reporting your answer.

3.16

Sample mean (M) = 50 Population mean (µ) = µM = 47 Sample standard deviation (s) = 4 Sample size (N) = 25 Based on this information, compute the t statistic for a one-sample t test. (You may need to compute some other values before computing the t statistic itself). When reporting your t statistic, please provide two decimal places.

3.75

Sample mean (M) = 78.6 Population mean (µ) = µM = 77 Population standard deviation (σ) = 10 Standard error (σM) = 1 Sample size (N) = 100 Based on this information, how much power would a researcher have to correctly reject the null hypothesis for a one-tailed test? For the purposes of this question, please make the following three assumptions: 1) The null hypothesis really is false. 2) The researcher is appropriately conducting a one-tailed z test with an alpha level of 0.05. The corresponding critical value that the researcher uses is z = 1.65. 3) The researcher is looking in the correct tail of the distribution. In other words, the researcher predicted that the sample mean (78.6) would be greater than the mean of the comparison population (77). Please report the power of the corresponding z test as a percentage with at least two decimal places. (You do not need to include the percent symbol with your answer).

48.01

Consider Z scores of + or - 1.96. What percentage of scores are at least as extreme as + or - 1.96 Z scores?

5.00%

Imagine that you have a normal distribution of scores with the following properties: mu=50, sigma=5. What is the value of the raw score in that distribution that would leave 20.05% of scores above it? Please provide at least one decimal place when reporting your answer.

54.2

When considering z scores of +or- 0.85 from the standard normal distribution, what percentage of the distribution of scores falls between those two z scores (i.e., +0.85 and -0.85)? Please provide your answer as a percentage with two decimal places. (You do not need to include the percent symbol).

60.46

Please refer back to your answer to question 10 and the information contained in that question. If the researcher were conducting a two-tailed hypothesis test with an alpha level of 0.05 (i.e., 5%), is the following statement true or false? Based on the two-tailed z test and the corresponding alpha level, the researcher has enough evidence to reject the null hypothesis that the two populations do not differ from one another.

False

Imagine that a researcher correctly conducts a two-tailed z test examining variable X with an alpha level (also called a p level) of 0.05 (5%). The researcher then correctly computes the following 95% confidence interval for variable X: [55.25, 59.75] Based on that information, would the researcher have enough evidence to reject the null hypothesis that the population he sampled from has a mean of 59 for variable X?

No. The researcher does not have enough evidence to reject the null hypothesis.

What are the critical values for a two-tailed single-sample T Test with a sample size of 25, and an alpha of 0.05 (5%)?

+or- 2.064

For a one-tailed Z test with alpha = 0.05, what is the absolute value of our critical value (as a Z score)?

1.645

What is the absolute value of the critical value for a one-tailed single-sample T Test with a sample size of 19, and an alpha of 0.05 (5%)?

1.734

Imagine that a researcher appropriately collects data from 100 people from a particular population for variable X. He obtains a mean of 45.9 from these 100 people. He also knows that the population mean for variable X is 45 (μ=45) with a standard deviation of 5 (σ=5). Using this information, compute the appropriate z statistic. For this question, please assume that all of the appropriate assumptions for a z test are met. Please report the correct z static below with two decimal places (if relevant).

1.80

For a two-tailed Z test with alpha = 0.05, what is the absolute value of our critical value (as a Z score)?

1.96

When conducting a two-tailed z test with an alpha level of 0.05 (i.e., 5%), what is the absolute magnitude of the corresponding critical value? Please provide only the absolute magnitude of the critical value (as a z statistic) when reporting your answer (i.e., don't worry about including a positive or negative sign). Please include two decimal places when providing your answer.

1.96

When considering a z score of -0.29 from the standard normal distribution, what percentage of the distribution of scores falls between the mean and that z score? Please provide your answer as a percentage with two decimal places. (You do not need to include the percent symbol).

11.41

What would be the critical value for a two-tailed, one-sample t test with df = 26 and alpha (p level) = 0.05? Please provide three decimal places when reporting your answer.

2.056

When considering a z score of -1.15 from the standard normal distribution, what percentage of the distribution of scores falls above that z score? Please provide your answer as a percentage with two decimal places. (You do not need to include the percent symbol).

87.49

What percentage of scores will be higher than a Z score of -1.20?

88.49%

Sample mean (M) = 95 Population mean (µ) = 100 Population standard deviation (σ) = 18 Sample size (N) = 144 What is the lower endpoint for the corresponding 95% confidence interval?

92.03

When considering a z score of 1.42 from the standard normal distribution, what percentage of the distribution of scores falls below that z score? Please provide your answer as a percentage with two decimal places. (You do not need to include the percent symbol).

92.22