Stats For Psych Study Guide With Answers PDF

1. Kesha, a renowned statistician and pop icon, is conducting a study to assess whether the preference for Flaming Hot Cheetos varies significantly among three age groups: teenagers, young adults, and older adults. Which statistical test should she use, and why is it preferred over multiple independ...

1. Kesha, a renowned statistician and pop icon, is conducting a study to assess whether the preference for Flaming Hot Cheetos varies significantly among three age groups: teenagers, young adults, and older adults. Which statistical test should she use, and why is it preferred over multiple independent-measures t-tests when comparing more than two independent groups? A) Independent-measures t-test; it compares two different groups, but using it multiple times increases Type I error risk and doesn’t account for variability across all groups simultaneously. B) One-way ANOVA; it compares means across multiple groups, reduces the risk of accumulating Type I errors, and analyzes variability both between and within groups. C) Paired t-test; it compares the same group before and after treatment, requires dependent samples, and is not suitable for comparing more than two groups. D) Simple mean comparison; it compares group means without statistical testing, ignores variability, and does not control for Type I errors when multiple comparisons are made. 2. Britney Spears, also a dedicated statistician, wants to compare the average consumption of Sour Patch Kids between fans attending her concerts and Kesha’s concerts. She decides to use an independent-measures t-test. How should she calculate the pooled standard deviation, and why is the pooled variance used when comparing two independent groups? A) By averaging the standard deviations of both groups; it assumes equal variances, simplifies the calculation, and combines the variability into a single estimate. B) By combining the variances of both groups weighted by their sample sizes; it fairly averages variability, accounts for unequal sample sizes, and provides a more accurate pooled variance. C) By using the larger standard deviation of the two groups; it provides a conservative estimate, accounts for maximum variability, and avoids underestimating the variance. D) By adding the standard deviations of both groups; it increases the overall variance estimate, does not consider sample sizes, and may overstate variability. 3. During a snack tasting event, participants sample both Flaming Hot Cheetos and Sour Patch Kids. To calculate the 95% confidence interval for the difference in satisfaction levels between the two snacks when the population standard deviations are unknown, which method should be used, and why? A) Use the t-score with the pooled standard deviation and sample sizes; it accounts for unknown population standard deviations, assumes equal variances, and uses degrees of freedom based on combined sample sizes. B) Use the t-score with individual standard deviations and sample sizes; it does not pool variances, allows for unequal variances, and adjusts degrees of freedom accordingly. C) Use the sample means directly without considering standard deviations; it ignores variability, may lead to inaccurate intervals, and assumes no variability between samples. D) Use the t-score with estimated population variances and sample sizes; it estimates variability, accounts for small samples, and uses degrees of freedom based on sample sizes minus one each. 4. Kesha and Britney are analyzing the differences in snack preferences. How should they calculate the degrees of freedom in their independent-measures t-test, and why is this important for determining the critical value? A) Add the sample sizes of both groups; it maximizes degrees of freedom, increases statistical power, and simplifies the calculation. B) Add the sample sizes and subtract one; it adjusts for estimating one parameter, impacts the critical value, and may not account for both samples. C) Add the sample sizes and subtract two; it accounts for estimating two means, affects the critical value from the t-distribution, and is standard for independent-measures t-tests. D) Use the smaller of the two sample sizes minus one; it provides a conservative estimate, ensures validity when variances are unequal, and adjusts for unequal sample sizes. 5. If Kesha wants to compare the average number of Flaming Hot Cheetos consumed by two groups, and the sample sizes are small with unknown population standard deviations, which test should she use, and why does this test account for these conditions? A) Use an independent-measures t-test; it is suitable for small samples, uses sample standard deviations to estimate population variability, and compares two independent groups. B) Use a paired t-test; it compares dependent samples, requires known population variances, and is not appropriate for independent groups. C) Use a large-sample approximation method; it assumes large samples, may not be accurate for small samples, and relies on normality. D) Use a standard deviation comparison; it focuses on variability, ignores means, and is insufficient for testing differences in averages. 6. During a promotional event, Kesha wants to determine if there’s a significant difference in the enjoyment ratings of her new song among fans who eat Flaming Hot Cheetos versus those who eat Sour Patch Kids. Which formula should she use to calculate the test statistic in an independent-measures t-test using pooled variance? A) Divide the difference in sample means by the pooled standard deviation multiplied by the square root of the sum of the reciprocals of the sample sizes; this accounts for pooled variability, sample sizes, and estimates standard error of the mean difference. B) Divide the difference in sample means by the square root of the sum of the variances divided by their respective sample sizes; this uses individual variances, accounts for unequal variances, and calculates the standard error directly. C) Divide the difference in sample means by the pooled standard deviation multiplied by the sum of the sample sizes; this ignores the reciprocal, overestimates standard error, and doesn’t adjust for sample sizes properly. D) Divide the difference in sample means by the pooled variance; this neglects to take the square root, disregards sample sizes, and results in an incorrect test statistic. 7. Britney observes that the distribution of preference scores for Sour Patch Kids has thicker tails compared to a normal distribution. Which statement is true about the t-distribution that can help her understand this observation, and how does it relate to sample size? A) It is symmetric and has thinner tails than the normal distribution; this indicates less variability and is typical with large sample sizes. B) It is skewed and has thicker tails than the normal distribution; this reflects asymmetry and is common with small sample sizes. C) It is symmetric and has thicker tails than the normal distribution; this accounts for increased variability with small sample sizes and unknown population standard deviations. D) It converges to a uniform distribution as degrees of freedom increase; this implies equal probabilities and is unrelated to the current scenario. 8. While analyzing the data, Kesha needs to calculate the pooled standard error for the independent-measures t-test. Which approach should she use, and why is it important for estimating the standard error of the difference between means? A) Calculate the square root of the sum of the variances divided by their sample sizes; it directly uses individual variances, accounts for unequal variances, and estimates standard error without pooling. B) Multiply the pooled standard deviation by the square root of the sum of the reciprocals of the sample sizes; it combines variability, adjusts for sample sizes, and provides the standard error needed for the t-test. C) Calculate the square root of the pooled variance multiplied by the sum of the sample sizes; this ignores reciprocals, may overestimate standard error, and doesn’t adjust properly for sample sizes. D) Add the standard deviations of both groups; this overestimates variability, doesn’t account for sample sizes, and isn’t appropriate for calculating standard error. 9. If Britney’s calculated t-statistic for the difference in average concert satisfaction between her fans and Kesha’s fans is greater than the critical value, what should she conclude regarding the null hypothesis and the significance of her findings? A) Fail to reject the null hypothesis; there is insufficient evidence of a difference, and the observed effect is likely due to chance. B) Reject the null hypothesis; there is a significant difference between the groups, the effect is unlikely due to chance, and her findings are statistically significant. C) Accept the null hypothesis; it is proven that there is no difference, and no further analysis is needed. D) Increase the sample size; the current sample is inadequate, the test is inconclusive, and more data is required. 10. Kesha is conducting a one-way ANOVA to compare the popularity of three snack brands among her concert attendees: Flaming Hot Cheetos, Sour Patch Kids, and regular Cheetos. Which of the following is not an assumption of one-way ANOVA that she should consider, and why? A) The samples are independent; this ensures observations in one group do not influence another, which is essential for valid results. B) The populations have equal variances; this assumption of homogeneity of variance allows for pooling variances and accurate F-statistic calculation. C) The populations are normally distributed; this ensures the validity of significance testing, especially with small sample sizes. D) The sample sizes are equal; while equal sizes are ideal, ANOVA can handle unequal sample sizes without violating assumptions. 11. To calculate the F-statistic in her ANOVA, what must Kesha do with the variances, and how does this help determine if group differences are significant? A) Compute the ratio of within-group variance to between-group variance; this assesses variability within groups, but does not test group differences directly. B) Compute the ratio of between-group variance to within-group variance; this compares variability due to group differences against variability within groups, helping determine significance. C) Divide the sum of squares within by the degrees of freedom within; this calculates mean square within but doesn’t directly provide the F-statistic. D) Subtract the within-group variance from the total variance; this isolates between-group variance but doesn’t form the F-ratio. 12. If the p-value in Britney’s ANOVA comparing dance move ratings is less than 0.05, what should she conclude about the group means and the next steps in her analysis? A) There is no significant difference between group means; she should accept the null hypothesis and conclude the dance moves are equally rated. B) At least one group mean is significantly different from the others; she should reject the null hypothesis and consider conducting post hoc tests to identify specific differences. C) All group means are significantly different from each other; she can conclude that every dance move is rated uniquely and no further tests are needed. D) Increase the sample sizes for more accurate results; the current p-value indicates insufficient data and inconclusive results. 13. As Kesha increases her sample size in testing whether Flaming Hot Cheetos consumption affects enjoyment of her music, what happens to the t-distribution she uses, and how does this affect her statistical analysis? A) It becomes more skewed; this increases the difficulty of analysis and affects critical values. B) It becomes more flattened; this reduces the variability and may lead to narrower confidence intervals. C) It approaches the normal distribution; critical values become closer to those of the normal distribution, which can impact hypothesis testing. D) It becomes bimodal; this introduces multiple peaks and complicates the interpretation of results. 14. When Britney conducts an independent-measures t-test, what is one key assumption she must ensure about her samples, and why is it important for the validity of her test? A) Samples are independent and come from populations with equal variances; this ensures accurate estimation of pooled variance, valid test statistics, and reliable p-values. B) The samples have equal means; this satisfies the null hypothesis and simplifies calculations but is not an assumption for conducting the test. C) The samples have equal sample sizes; while beneficial, it is not a strict requirement and doesn’t impact the test’s validity significantly. D) The samples are dependent; this contradicts the independent-measures design and violates the test’s fundamental assumptions. 15. Kesha wants to create a 95% confidence interval for the difference in average dance scores between two of her performances. Which factor does not affect the width of this confidence interval, and why? A) Sample sizes; larger samples reduce standard error and narrow the confidence interval. B) Pooled standard deviation; greater variability increases standard error and widens the interval. C) Confidence level; higher confidence levels widen the interval to ensure the parameter lies within it. D) The actual difference between the population means; the interval estimates this difference, but its width is determined by variability and sample size, not the true mean difference. 16. Britney is testing if there’s no difference in popularity between Flaming Hot Cheetos and Sour Patch Kids among her fans. Which null hypothesis should she use in her independent-measures t-test, and how does it reflect her research question? A) The mean preference for Flaming Hot Cheetos is greater than for Sour Patch Kids; this implies a directional difference and is an alternative hypothesis. B) The mean preferences for Flaming Hot Cheetos and Sour Patch Kids are not equal; this suggests a difference exists and represents the alternative hypothesis. C) The mean preference for Flaming Hot Cheetos is less than for Sour Patch Kids; this is directional and aligns with an alternative hypothesis. D) The mean preferences for Flaming Hot Cheetos and Sour Patch Kids are equal; this states no difference exists and serves as the null hypothesis. 17. To calculate the pooled variance in her t-test comparing two groups of fans, how should Kesha proceed, assuming equal variances, and why is this method appropriate? A) Combine the variances of both groups by weighting them according to their degrees of freedom; this accounts for sample sizes, provides an accurate pooled estimate, and assumes equal population variances. B) Average the variances of both groups; this treats samples equally regardless of size, may not be accurate with unequal sample sizes, and assumes equal variances. C) Take the square root of the sum of the variances divided by their sample sizes; this method calculates standard error but not pooled variance directly. D) Add the variances of both groups divided by their sample sizes; this doesn’t weight by degrees of freedom and may not provide an accurate pooled variance. 18. Britney wants to increase the power of her t-test comparing concert satisfaction between fans who received free snacks and those who didn’t. Which action should she take, and how does it affect the components of the test? A) Decrease the sample sizes; this increases standard error, reduces power, and makes it harder to detect a true effect. B) Increase the sample sizes; this reduces standard error, increases power, and enhances the likelihood of detecting a significant difference if one exists. C) Use a higher significance level (e.g., from 0.05 to 0.10); this increases Type I error risk, may not affect power significantly, and could lead to false positives. D) Increase the pooled standard deviation; this increases variability, reduces power, and makes detecting differences more difficult. 19. In Kesha’s one-way ANOVA comparing the effectiveness of different dance routines, into what components is the total sum of squares divided, and how does this partitioning aid in the analysis? A) Between-group sum of squares and within-group sum of squares; this partitions variance into components due to group differences and random error within groups, facilitating the F-test. B) Between-group sum of squares and total sum of squares; this does not account for within-group variability and is incomplete for ANOVA. C) Within-group sum of squares and error sum of squares; these are the same in ANOVA, so this partitioning is redundant. D) Total sum of squares and regression sum of squares; this terminology is specific to regression analysis, not ANOVA. 20. As Britney increases the sample size in her hypothesis testing about snack preferences, what happens to the t-distribution she uses, and how does this influence her critical values and confidence intervals? A) The standard error increases; this is incorrect as larger samples reduce standard error. B) The confidence interval becomes wider; larger samples decrease variability, leading to narrower intervals. C) The t-distribution approaches the standard normal distribution; critical values become closer to those of the normal distribution, affecting hypothesis testing and interval estimation. D) The population mean changes; increasing sample size does not affect the population parameter but improves the estimate’s accuracy.