Psych 2220 - Exam 2 Homework 3 + 4

Which of the following actions would increase statistical power for a z test? Please choose all correct answers below. For each option, please assume that only the factor mentioned changes (i.e., all other factors remain constant).

- Correct! Increase alpha from 0.05 to 0.10. - Correct! Increase the sample size. - Increase the population standard deviation. - Decrease the mean difference between the relevant sampling distributions, thereby causing the distributions to overlap to a greater degree.

Which of the following statements are true for a distribution of means? (When answering, please assume that the sample size for each mean is equal to 80 and that all scores are drawn from the same population of scores). Please select all correct answers.

- Correct! The distribution of means has less variability than the corresponding population of scores. - The distribution of means has more variability than the corresponding population of scores. - Correct! The distribution of means has the same mean (average) as the population of scores. - Correct! If the population of scores is not normally distributed, the distribution of means should be more normally distributed than the population of scores.

Imagine that a researcher appropriately collects data from 100 people from a particular population for variable X. He obtains a mean of 19.2 from these 100 people. He also knows that the population mean for variable X is 21.05 (μ = 21.05) with a population standard deviation of 10 (σ = 10). If the researcher uses a two-tailed hypothesis test with an alpha level (or p-level) of 0.05 (5%), what decision should the researcher make when following the rules of hypothesis testing? (When answering, please assume that any relevant assumptions are met for this hypothesis test).

- Reject the null hypothesis - Correct! Fail to reject the null hypothesis - In order to choose one of the answers listed above, more information would have to be provided as part of the question.

Which of the following are assumptions of the z test? Please select all correct answers.

- The independent variable is measured as a scale variable. - Correct! The dependent variable is measured as a scale variable. - Correct! Participants are randomly selected from the population. - Correct! The population of interest is normally distributed.

Imagine that a researcher appropriately conducts a z test and then calculates a corresponding 95% confidence interval. When calculating that 95% confidence interval, the researcher should center the confidence interval on... Please choose the best option that correctly completes the sentence fragment.

- The population mean (µ). - Correct! The sample mean (M). - The population standard deviation.

Which of the following correctly describes a standard error?

- The standard error is always equal to the variance of the corresponding population. - Correct! The standard error is what we call the standard deviation for a distribution of means (from a particular population and with a specific sample size). - The standard error must be greater in magnitude than the corresponding population standard deviation. - All of the above. - None of the above.

Imagine that a researcher obtains a mean value of 40 on variable X, and that the corresponding distribution of means has a grand mean (or overall mean) of 44 ( µM = 44). Based on this information, what can we know about the corresponding z statistic?

- The z statistic must be larger than 4.00. - The z statistic must be fall between the values 0 and 10.00. - The z statistic must be a positive z statistic. - Correct! The z statistic must be a negative z statistic. - We can not know any of the statements listed above with out also knowing the value of the standard error.

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? Please choose the correct response option below.

- Yes. The researcher has enough evidence to reject the null hypothesis. - Correct! No. The researcher does not have enough evidence to reject the null hypothesis. - The hypothesis test and the 95% confidence interval provide entirely different information. The 95% confidence interval can not be used to know if a hypothesis test would lead to a rejection of the null hypothesis. - Maybe, but our conclusion would depend upon the magnitude of the standard error. Because the standard error was not explicitly provided, we can not know if the researcher has enough evidence to reject the null hypothesis.

Imagine that a researcher conducts a one-tailed z test with an alpha level (also called a p-level) of 0.05 (5%). What is the absolute value of the critical value for the corresponding hypothesis test? When answering, please provide at least two decimal places (if relevant).

1.645

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 z statistic. Please report the correct z statistic below with two decimal places (if relevant).

1.8

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). You should use the z table when answering this question.

11.41

When considering z scores of ±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). You should use the z table when answering this question.

21.12

According to Cohen's guidelines, an effect size of d = 0.50 would be a ____________ effect. Please type the correct missing term into the blank above.

medium/moderate

Imagine that a researcher studies a population of 1000 people. Within this population, heights (measured in inches) are normally distributed. Please assume that the mean height for this population is 68 inches with a population standard deviation of 4 inches. Under these conditions, what z score would correspond to a height of 71 inches? Please report the correct z score below with two decimal places (if relevant).

0.75

Please consider the following information: 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

Please consider the following information: 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

Imagine that you have a normal distribution of scores with the following properties: Population mean = 50 ( μ = 50 ) Population standard deviation = 5 ( σ = 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 ±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). You should use the z table when answering this question.

60.46

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). You should use the z table when answering this question.

87.49

Please consider the following information: Sample mean (M) = 95 Population mean (µ) = 100 Population standard deviation (σ) = 18 Sample size (N) = 144 Based on this information, what is the lower endpoint (denoted Mlower in the textbook) for the corresponding 95% confidence interval? Please include two decimal places when reporting your answer.

92.06

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). You should use the z table when answering this question.

92.22