IOP 201-Q (Industrial Psychological Research) Tutorial 6

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1 IOP 201-Q (Industrial Psychological Research) Tutorial 6 TRUE/FALSE [1 point each] Indicate whether the sentence or statement is true or false. 1. Probability values are always greater than or equal to zero. 2. Sampling with replacement means that it is possible for the same individual to be selected more than once for a single sample. 3. One major advantage of transforming X values into z-scores is that the z-scores always form a normal distribution. 4. When the z-score value in a normal distribution is negative, the body of the distribution is on the right-hand side. 5. For any normal distribution, exactly 2.5% of the scores are located in the tail beyond z = It is possible for the distribution of sample means to be normal even if it is based on samples with less than n = A sample mean with a z-score value between 0.50 and would be considered a fairly typical, representative sample. 10. The null hypothesis always concerns a population even though the data come from a sample. 11. A Type II error occurs when a treatment actually does have an effect on the scores but the effect fails to show up in a research study. 12. There is always a possibility that the decision reached in a hypothesis test is incorrect. 13. The t statistic is used for hypothesis tests in situations where the population standard deviation (or variance) is unknown. 14. In a t statistic, the estimated standard error provides a measure of how much difference is reasonable to expect between a sample mean and the population mean. 15. As sample size increases, the estimated standard error tends to decrease. 16. To calculate a t statistic, you must first compute the sample mean and the sample variance (or sample standard deviation). 17. Assuming all other factors are held constant, t statistics tend to be more variable than z-scores. 18. While conducting a two-tailed hypothesis test, a researcher obtains a t statistic of t = 2.10 for a sample of n = 15. The researcher should reject the null hypothesis with α = In general, an increase in the sample variance will produce an increase in the magnitude of the t statistic. 20. The null hypothesis for an independent-measures t test states that the two sample means are equal. 21. For an independent-measures t statistic, the magnitude of the estimated standard error is inversely related to the size of the samples (the bigger the samples, the smaller the error). 23. If an independent-measures t statistic has df = 19, then it is impossible for the two samples to be the same size.

2 25. When a researcher reports a "significant difference" between two treatments based on the outcome of an independent-measures t hypothesis test, it means that there is a very large difference between the two treatments. 27. Estimated standard error for a repeated-measures t statistic is based on the variance of the difference scores. 28. The larger the variance of the difference scores, the larger the standard error for the repeated-measures t. 29. A repeated-measures t statistic with df = 20 indicates that a total of 21 subjects participated in the research study. 30. A general concern for researchers using a repeated-measures design is that the participants' scores in the second treatment may be influenced by aftereffects from the first treatment.

3 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 31. Probability values are always. A Greater than or equal to zero B Less than or equal to one C Positive numbers 32. For a normal distribution, the proportion in the tail beyond z = 1.50 is p = Based on this information, what is the proportion in the tail beyond z = 1.50? A B C D What proportion of the scores in a normal distribution have z-scores greater than z = -1.25? A B C D For a normal distribution, what z-score value separates the highest 10% of the distribution from the lowest 90%? A z = 0.90 B z = 0.90 C z = 1.28 D z = What proportion of a normal distribution is located between z = 1.16 and z = +1.16? A B C D For a normal distribution with a mean of µ = 40 and σ = 4, what is the probability of sampling an individual with a score less than 46? A B C D

4 37. A normal distribution has a mean of µ = 500 and σ = 100. What score is needed to place in the top 20% of the distribution? A 520 B 580 C 584 D The symbol that corresponds to the standard error of x is. A σ x B µ C σ D x x 39. When the sample size is greater than n = 30. A The distribution of sample means will be approximately normal B The sample mean will be equal to the population mean C All of the above D None of the above 40. If you select a random sample of n = 16 scores from a population with µ = 70 and σ = 20, how much error would you expect, on average, between the sample mean and the population mean? A 1.25 points B 4 points C 5 points D 20 points 41. A normal population has µ = 50 and σ = 8. A random sample of n = 4 scores from this population has a mean of 54. What is the z-score for this sample mean? A B C D A random sample is obtained from a population with µ = 80 and σ = 10. Which of the following samples would have the largest z-score? A n = 25 with x = 82 B n = 25 with x = 84 C n = 100 with x = 82 D n = 100 with x = 84

5 43. If sample size (n) is held constant, the standard error will as the population variance increases. A Increase B Decrease C Stay constant D Cannot answer with the information given 44. The final step of hypothesis testing is to. A Locate the values associated with the critical region B Make a statistical decision about H 0 C Collect the sample data and compute the test statistic D State the hypotheses and select an alpha level 45. In a hypothesis test, a z-score value near zero _. A Is probably in the critical region B Means that you should probably reject the null hypothesis C Is strong evidence of a statistically significant effect E None of the above 46. A Type I error means that a researcher has. A Falsely concluded that a treatment has an effect B Correctly concluded that a treatment has no effect C Falsely concluded that a treatment has no effect D Correctly concluded that a treatment has an effect 47. A researcher risks a Type I error. A Anytime H 0 is rejected B Anytime H 1 is rejected C Anytime the decision is "fail to reject H 0 " 48. By selecting a smaller alpha level, a researcher is. A Attempting to make it easier to reject H 0 B Better able to detect a treatment effect C Reducing the risk of a Type I error 49. The major difference between the t statistic formula and the z-score formula is. A The t statistic uses the sample variance in place of the population variance B The t statistic uses the sample mean in place of the population mean C The t statistic computes standard error by dividing the standard deviation by df = n 1 instead of dividing by n

6 50. What is the estimated standard error for a sample of n = 9 scores with s 2 = 36? A B C D 51. With α =.01, the one-tailed critical region for a sample of n = 30 would have a boundary of. A t = B t = C t = D t = A sample has a mean of x = 39.5 and a standard deviation of s = 4.3. In a two-tailed hypothesis test with α =.05, this sample produces a t statistic of t = Based on this information, the correct statistical decision is. A Reject the null hypothesis B Fail to reject the null hypothesis C Cannot answer without additional information 53. For a sample of n = 15, what t values determine the two-tailed critical region for α =.05? A , B , C , D , Two samples from the same population both have n = 10 scores with X = 45. If t statistics are computed for these two samples, then. A The two t statistics will be identical B The sample with the larger variance will produce the larger t statistic C The sample with the smaller variance will produce the larger t statistic 55. Which of the following research situations is most likely to use an independent-measures design? A Evaluate the effectiveness of a diet program by measuring how much weight is lost during 4 weeks of dieting. B Evaluate the effectiveness of a cholesterol medication by comparing cholesterol levels before and after the medication. C Evaluate the difference in verbal skills between 3-year-old girls and 3-year-old boys. D Evaluate the development of verbal skills between age 2 and age 3 for a sample of girls.

7 56. Two samples, each with n = 6 subjects, produce a pooled variance of 20. Based on this information, the estimated standard error for the sample mean difference would be. A 20/6 B 20/12 C D The results of an independent-measures research study are reported as "t(5) = 2.12, p >.05, two tails." For this study, what t values formed the boundaries for the critical region? A and B and C and D Cannot be determined from the information given 58. A research study uses n = 6 subjects in treatment 1 and a separate sample of n = 6 subjects in treatment 2. For this study the independent-measures t statistic has degrees of freedom equal to. A 10 B 5 C 12 D For a repeated-measures hypothesis test, the null hypothesis states. A d x = 0 B µ d = 0 C µ 1 = µ 2 D d = d x 1 x A repeated-measures experiment and a matched-subjects experiment both produce t statistics with df = 20. Which experiment used more subjects? A Repeated measures B Matched subjects C They both used n = 21 subjects. D They both used n = 22 subjects. 61. For which of the following situations would a repeated-measures design have the maximum advantage over an independent-measures design? A When many subjects are available and individual differences are small B When very few subjects are available and individual differences are small C When many subjects are available and individual differences are large D When very few subjects are available and individual differences are large

8 62. With α =.05 and a sample of n = 12 subjects in a repeated-measures experiment, the critical region for the t statistic has boundaries of. A t = ±2.228 B t = ±1.812 C t = ±1.796 D t = ± In general, what characteristics of the data (difference scores) are most likely to produce a significant t statistic for the repeated-measures hypothesis test? A A large mean difference and large variance B A large mean difference and small variance C A small mean difference and large variance D A small mean difference and small variance

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