Bowie State University Statistics Worksheet

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Bowie state university Department of psychology Statistics I Assignment 3 Hypothesis Testing 50 points This assignment is due on April 27, 2020 at 11:59pm Please answer the questions by coloring or writing the answer only for each question Turn in on the blackboard drop box of assignment and tests Name _____________________________________________ Multiple Choice 1. Although their formulas are similar, one difference between the z-score (z) and the t-statistic (t) is that ______. a. only the denominator of the z-score formula (not the t-statistic) is a measure of variability b. z-scores evaluate sample means whereas t-statistics evaluate individual scores c. only the numerator of the z-score formula (not the t-statistic) is the difference between means d. the z-score evaluates individual scores whereas the t-statistic evaluates sample means 2. Which of the following is a similarity of the t-distribution and the standard normal distribution? a. There is only one distribution for each. b. Both distributions are symmetrical. c. Both distributions are asymmetrical. d. Both distributions are a function of the sample size. 3. A researcher draws a random sample of 25 people from a population and calculates the mean of their IQs. If she were to repeat this process of drawing samples and calculating means an infinite number of times, the sample means could be used to create ______. a. the sampling distribution of the mean b. critical values c. z-scores d. research hypotheses 4. The sampling distribution of the mean helps ______. a. determine the probability of obtaining a particular value of the population mean (µ) b. describe the modality of a set of data c. determine whether a set of data is skewed (asymmetric) X d. determine the probability of obtaining a particular value of a sample mean 5. Holding all else constant, as sample size increases, the sampling distribution of the mean ______. a. becomes flatter b. has greater variability ( ) c. becomes skewed d. becomes more peaked 6. The modality, symmetry, and variability of the sampling distribution of the mean are defined by a statistical principle known as ______. a. random sampling b. ratio scale of measurement c. standard error of the mean d. central limit theorem 7. What is the sufficient sample size to use for the central limit theorem? a. at least 25 b. at least 26 c. at least 30 d. at least 31 8. Standard deviation measures the ______ for a variable, standard error represents the ______ calculated from samples. a. variability of statistics; variability of scores b. variability of scores; variability of statistics c. variability of scores; error of scores d. variability of statistics; error of scores 9. Which of the following is a correctly stated null hypothesis? a. H0: µ ≠ 3 b. H0: X = 3 c. H0: µ = 3 d. H0: X = 3 10. Which of the following is a correctly stated alternative hypothesis? a. H1: µ ≠ 3 b. H1: µ = 3 c. H1: X = 3 d. H1: X > 3 11. The statement “µ ≠ 3” would be part of a ______. a. two-tailed, directional hypothesis b. two-tailed, non-directional hypothesis c. one-tailed, directional hypothesis d. one-tailed, non-directional hypothesis 12. The statement µ > 3 is an example of a ______. a. directional (one-tailed) null hypothesis b. directional (one-tailed) alternative hypothesis c. non-directional (two-tailed) null hypothesis d. non-directional (two-tailed) alternative hypothesis 13. The ‘>’ symbol would appear in the ______ hypothesis and would imply that this hypothesis is ______. a. null; non-directional b. null; two-tailed c. alternative; one-tailed d. alternative; non-directional 14. A ‘≠’ symbol in the ______ hypothesis implies this hypothesis is ______. a. null; directional b. null; two-tailed c. alternative; one-tailed d. alternative; non-directional 15. This distribution provides an illustration of a ______. a. one-tailed null hypothesis b. directional null hypothesis c. directional alternative hypothesis d. two-tailed alternative hypothesis 16. This distribution illustrates a ______. a. non-directional null hypothesis b. directional null hypothesis c. non-directional alternative hypothesis d. directional alternative hypothesis 17. The decision to use a directional versus non-directional alternative hypothesis most directly affects ______. a. the critical value(s) b. alpha () c. the sample size d. the degrees of freedom 18. Imagine that for a population of 200, the mean is 20.23 with a standard deviation of 5.12. What ( ) is the population standard error of the mean X ? a. .003 b. .03 c. .36 d. .50 19. Imagine that for a population of 40, the mean is 10.25 with a standard deviation of 2.10. What ( ) is the population standard error of the mean X ? a. .03 b. .33 c. .34 d. .36 20. A population has a mean of 15.21 and a standard deviation of 1.56. For a sample of N = 20, ( ) what is the population standard error of the mean X ? a. .35 b. .36 c. 1.56 d. 4.47 21. A population has a mean of 55.25 and a standard deviation of 14.23. For a sample of N = 100, ( ) what is the population standard error of the mean X ? a. 7.03 b. 3.77 c. 1.43 d. 1.42 22. A population has a mean of 606 and a standard deviation of 23. For a sample of N = 500, what ( ) is the population standard error of the mean X ? a. .10 b. 1.02 c. 1.03 d. 1.1 23. Using the following information, calculate the z-statistic for the z-test for one mean. X = 15 μ = 22 ( X ) = 3.50 a. 2.00 b. –2.00 c. 1.23 d. –3.13 24. Using the following information, calculate the z-statistic for the z-test for one mean. X = 27 μ = 15 X = 1.50 a. –8.00 b. 8.00 c. 4.00 d. –.10 25. Using the following information, calculate the z-statistic for the z-test for one mean. X = 154 μ = 145 X = 15.25 a. 9.00 b. –9.00 c. .59 d. –.59 26. Using the following information, calculate the z-statistic for the z-test for one mean. X = 31.75 μ = 25.67 X = 2.45 a. 2.48 b. –2.48 c. .10 d. -.10 27. Using the following information, calculate the z-statistic for the z-test for one mean. X = 101 μ = 109 X = 3.44 a. –2.32 b. 2.32 c. –2.33 d. 2.33 28. If the calculated value of a z-statistic ______ the critical value, you would say ______. a. does not exceed; p < .01 b. does not exceed; p < .05 c. does not exceed; p > .05 d. exceeds; p > .05 29. A researcher has calculated a z-statistic of 1.92. For a two-tailed test with alpha () = .05, which of the following is the most appropriate? a. do not reject the null (p < .05) b. do not reject the null (p > .05) c. reject the null (p < .05) d. reject the null (p > .05) 30. For a z-statistic of 1.89, one would conclude (for a two-tailed test) the score is ______. a. significant only at the .05 level b. significant at both the .05 level and the .01 level c. not significant d. not significant at the .05 level but is significant at the .01 level 31. For a z-statistic of –1.34, one would conclude (for a two-tailed test) the score is ______. a. significant at the .05 level but not the .01 level b. significant at both the .05 level and the .01 level c. not significant d. not significant at the .05 level but is significant at the .01 level 32. Reporting the results of a z-test results typically includes all of the following EXCEPT ______. a. the variable analyzed b. the standard error of the sample mean c. the sample and population means d. the level of significance 33. From data collected from a sample of 100 people, you obtain a mean of 16.27 and a standard (s ) deviation of 4.56. What is the value for the standard error of the mean X ? a. .46 b. .05 c. .16 d. 4.56 34. You collect data from a sample of 150 people, and calculate a mean of 6.87 and a standard (s ) deviation of 3.69. What is the value for the standard error of the mean X ? a. .30 b. 1.86 c. 6.87 d. 21.83 35. If I wanted to measure the variability of ______ , I would calculate ______. (s ) a. individual scores (Xs); the standard error of the mean X Xs (s ) b. sample means ; the standard error of the mean X Xs c. sample means ; the standard deviation (s) X d. individual scores (Xs); the sample mean X 36. In testing the mean of a sample, the sample mean is transformed into a t-statistic in order to ______. a. determine the critical values b. prove our research hypotheses c. determine whether the alternative hypothesis (H1) should be one-tailed or two-tailed d. determine the probability of obtaining the value of the sample mean Ans: D X 37. In testing the mean of a sample, the sample mean is transformed into a ______ statistic in order to ______. a. z; decide whether to set alpha at .05 or .01 b. t; determine the probability of a sample mean c. z; determine the critical values d. t; determine whether the distribution of sample means is normal 38. In testing the mean of a sample, calculating a positive value of the t-statistic (t) necessarily implies ______. a. the research hypothesis has been supported b. you have done your calculations correctly (without making a mistake) c. the value of the t-statistic falls in the region of rejection d. the sample mean is greater than the hypothesized population mean 39. In testing the mean of a sample, calculating a negative value of the t-statistic (t) indicates ______. a. the sample mean is less than the hypothesized population mean b. the score is less than the mean ( ) ( ) ( ) ( ) ( ) c. X is greater than d. you have made an error in your calculations 40. Which of the following can be a negative number in testing the mean of a sample? a. t b. df s c. X d. α 41. Which of the following can be a negative number in testing the mean of a sample? a. the degrees of freedom b. the critical values c. alpha (s ) d. the standard error of the mean X 42. Looking at the ______ for a statistic like a t-statistic provides an indication of the sample size in a study. a. research hypothesis b. null hypothesis c. degrees of freedom d. alternative hypothesis 43. A researcher calculates a mean from a sample of 10 people. In analyzing her data, she states the following hypotheses: H0: μ = 30 and H1: μ ≠ 30. If α = .05, which of the following is an appropriate critical value? (Hint: Use the table in appendix) a. 1.833 b. 2.042 c. 2.228 d. 2.262 44. A researcher calculates a mean from a sample of 15 people. In analyzing her data, she states the following hypotheses: H0: μ = 25 and H1: μ ≠ 25. If α = .05, which of the following is an appropriate critical value? (Hint: Use the table in appendix) a. 1.709 b. 1.753 c. 2.060 d. 2.145 45. A researcher calculates a mean from a sample of 18 people. In analyzing her data, she states the following hypotheses: H0: μ = 20 and H1: μ ≠ 20. For α = .05, which is an appropriate critical value? (Hint: Use the table in appendix) a. 1.734 b. 2.110 c. 2.101 d. 2.086 46. A researcher calculates a mean from a sample of 23 people. In analyzing her data, she states the following hypotheses: H0: μ = 25 and H1: μ ≠ 25. For α = .05, which is an appropriate critical value? (Hint: Use the table in appendix) a. 1.717 b. 2.074 c. 2.069 d. 2.064 47. A researcher tests the mean of a sample of 25 people and calculates a value of 2.51 for the tstatistic. For α = .05 (two-tailed), which of the following is most appropriate? a. do not reject null (p < .05) b. do not reject null (p > .05) c. reject null (p < .05) d. reject null (p > .01) 48. A researcher tests the mean of a sample of 28 people and calculates a value of 2.13 for the tstatistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate? a. do not reject null (p < .05) b. do not reject null (p > .05) c. reject null (p < .05) d. accept null (p < .05) 49. You test the mean of a sample of 19 people and calculate a value of 2.14 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate? a. do not reject null (p > .01) b. reject null (p > .05) c. accept alternative (p > .05) d. reject null (p < .05) 50. A researcher calculates a value of 3.21 for a t-statistic. For df = 20 and alpha = .05 (two-tailed), which of the following is the MOST accurate? a. reject the null hypothesis b. p < .05 c. p < .01 d. do not reject the null hypothesis
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Hello there deedlebm! I already finished answering all the items of your assignment. For a good experience as a new tutor, please let me explain to you items 43 to 46 😀. As you can see in the problems, they are similar to each other. There are no given or any specified test that will be used in the problem. In this kind of question, you can easily determine what kind of test is appropriate to use. The samples are less than 30 and the standard deviation for each problem is not known. Meaning to say, you will use T-Test. For you to be able to find the critical values for each item, you have to locate it in T-Test Table ( I provided a T-Test table and uploaded it together with your assignment). Note that when finding the critical value, you must have to calculate the degree of freedom (df) that has a formula of n-1 where n is the sample given in the problem. Another important thing that you have to take note is choosing between one-tail and two-tail test in the table. Always use "Two-tail" test because it can determine if there is any significant difference between the groups you are comparing unless specified by your professor to use one-tail test. By using the table, the intersection between the degree of freedom df and the two-tail confidence level will be your critical value for t-statistics. I made sure that I was able to check my answers twice. The answers were highlighted (yellow). Thank you for trusting me 😀. I would be glad to work with you again. Goodluck to your studies ^__^Reference of the T-test table:https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf

Bowie state university
Department of psychology
Statistics I Assignment 3 Hypothesis Testing
50 points
This assignment is due on April 27, 2020 at 11:59pm
Please answer the questions by coloring or writing the answer only for each question
Turn in on the blackboard drop box of assignment and tests
Name _____________________________________________
Multiple Choice

1. Although their formulas are similar, one difference between the z-score (z) and the t-statistic (t)
is that ______.
a. only the denominator of the z-score formula (not the t-statistic) is a measure of
variability
b. z-scores evaluate sample means whereas t-statistics evaluate individual scores
c. only the numerator of the z-score formula (not the t-statistic) is the difference between
means
d. the z-score evaluates individual scores whereas the t-statistic evaluates sample means
2. Which of the following is a similarity of the t-distribution and the standard normal
distribution?
a. There is only one distribution for each.
b. Both distributions are symmetrical.
c. Both distributions are asymmetrical.
d. Both distributions are a function of the sample size.
3. A researcher draws a random sample of 25 people from a population and calculates the mean
of their IQs. If she were to repeat this process of drawing samples and calculating means an
infinite number of times, the sample means could be used to create ______.
a. the sampling distribution of the mean
b. critical values
c. z-scores
d. research hypotheses
4. The sampling distribution of the mean helps ______.
a. determine the probability of obtaining a particular value of the population mean (µ)
b. describe the modality of a set of data
c. determine whether a set of data is skewed (asymmetric)
...


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