Psych Stats_Exam 2 Practice Problems - Answers

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Feb 20, 2024

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1. Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). In a representative study, Professor Tortoriello collects a sample of n=100 adolescents with a history of group participation. The sample is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of μ=50 and a standard deviation of σ=15 . The sample of group- participation adolescents had an average of M=53.8 . Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with α = .05. z obtained = +2.53; +2.53 > +1.96; z obtained is in the critical region. Reject the null hypothesis. There is evidence that self-esteem scores for adolescents is significantly different from those of the general population. 2. Ackerman and Goldsmith (2011) report that students who study from a screen (smartphone, tablet, or computer) tended to have lower quiz scores than students who studied the same material from printed pages. To test this finding, Professor Tortoriello identifies a sample of n=16 students who used the electronic version of the course textbook and determines that this sample had an average score of M=72.5 on the final exam. During the previous three years, the final exam scores for the general population of students taking the course averaged μ=77 with a standard deviation of σ=8 and formed a roughly normal distribution. Professor T would like to use the sample to determine whether students studying from an electronic screen had exam scores that are significantly different from those for the general population. Using the standard four-step procedure, conduct a two-tailed hypothesis test with α=.05 to evaluate the effect of studying from an electronic screen. z obtained = -2.25; -2.25 < - 1.96; z obtained is in the critical region. Reject the null hypothesis. There is evidence that studying from a screen affects exam scores. 3. The following sample of n=5 scores was obtained from a population with unknown parameters. Scores: 20, 25, 30, 20, 30 Compute the sample mean and variance. M = 25, s 2 = 25 Compute the estimated standard error for M . S M = 2.24
4. Oishi and Schimmack (2010) report that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. To further examine this relationship, Professor Tortoriello obtains a sample of n=12 young adults who each experienced five or more different homes before they were 16 years old. These participants were given a standardized well-being questionnaire for which the general population has an average score of μ=40 . The sample of well-being scores had an average of M=37 and a variance of s 2 =10.73 . On the basis of this sample, is well-being for frequent movers significantly different from well- being in the general population? Use a two-tailed test with α=.05 . t obtained = -3.16; -3.16 < - 2.201; t obtained is in the critical region. Reject the null hypothesis. There is evidence that moving as a child affected well-being scores. Compute the estimated Cohen’s d to measure the size of the difference. d = 0.92 5. Two separate samples, each with n=9 individuals, receive different treatments. After treatment, the first sample has SS=546 and the second has SS=606 . Find the pooled variance for the two samples. s 2 P = 72 Compute the estimated standard error for the sample mean difference. s M1-M2 = 4.00 6. Does posting calorie content for menu items affect people’s choices in fast-food restaurants? According to results obtained by Elbel, Gyamfi, and Kersh (2011), the answer is no. The researchers monitored the calorie content of food purchases for children and adolescents in four large fast-food chains before and after mandatory labeling began in New York City. Although most of the adolescents reported noticing the calorie labels, apparently the labels had no effect on their choices. Data similar to the results obtained show an average of M=786 calories per meal with SS= 715,275 for n=100 children and adolescents before the labeling, compared to an average of M=772 calories with SS= 819,819 for a similar sample of n=100 children after the mandatory posting. Use a two-tailed test with α=.05 to determine whether the mean number of calories after the posting is significantly different than before calorie content was posted. t obtained = 1.12; 1.12 < 1.98; t obtained is not in the critical region. Fail to reject the null hypothesis. There was no significant change in calorie consumption after the mandatory posting. Calculat e r 2 to measure effect size for the mean difference. r 2 = 0.0063  
7. Even if a treatment has an effect, it is still possible to obtain a sample mean after the treatment that is very similar to the original population mean. Which outcome is likely if this happens?    a  reject H 0 and make a Type I error     correctly reject H 0     c   fail to reject H 0 and make a Type II error     d  correctly fail to reject H 0     8. One sample has a variance of s 2 = 12 and a second sample has a variance of s 2 = 8. Which of the following most accurately describes the pooled variance for the two samples?     a  closer to 8 than to 12     b  closer to 12 than to 8     c   somewhere between 8 and 12     d  around 16     9. A researcher is examining whether daily exercise influences mood. The researcher assigns n = 12 individuals to exercise for three months and finds an average mood score of M = 22 with SS = 182 after three months for individuals in this group . A second group of n = 7 individuals assigned to a control group for the three months has a mood score of M = 19 with SS = 90. Which of the following is most consistent with the results of conducting a two-tailed independent- measures t test with α = .05?     a   t = +2.12 and fail to reject the null hypothesis     b   t = +2.12 and reject the null hypothesis     c   t = +1.58 and fail to reject the null hypothesis     d   t = +1.58 and reject the null hypothesis     10. If a repeated-measures study shows a statistically significant difference between two treatments with α = 0.01, what can the researcher conclude about measures of effect size?     a  The value of Cohen’s d is large.     b  The value of Cohen’s d is small.     c  The value of both Cohen’s d and r 2 are large.     d   A statistically significant effect does not necessarily indicate that the effect size will be large.    
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