WGU STatistics Test Questions & Answers

In a standard 52-card deck, where each card is assigned a numeric value, the mean of the 52 cards is 7.0 with a standard deviation of 3.742. To test if a representative sample can be attained, the deck is shuffled and 13 cards are randomly drawn, one at a time. Each card is recorded and then returned randomly to the deck before the next card is drawn. This process of drawing 13 random cards is repeated a total of 20 times, and the mean and standard deviation of each round is computed. Which type of sampling is this an example of? Randomization Multiple comparison Matched pairs Bootstrap - ANSWERSBootstrap A study is done to determine if the color of an apple affects the purchase rate by consumers at a grocery store. Purchase counts for three colors of apples are collected. Which technique should be used to determine if there is a difference in purchase rate by color? Rank-based Randomization t-test ANOVA - ANSWERSANOVA A hospital network collects the amount of time it takes doctors to see patients. Which two techniques are appropriate to compare the mean times of two subsets within this set of doctors? Choose 2 answers ANOVA t-test Logistic regression Principal component analysis - ANSWERSANOVA t-test A data analyst needs to determine whether antioxidants in blackberries can reduce age-related cognitive decline. Twenty-five adults between 65 and 80 are selected to eat blackberries for six months and be retested. The original scores are compared with the second scores to determine whether there was decline. What is the appropriate model to test the hypothesis? z test ANOVA Linear regression Two-sample t-test - ANSWERSTwo-sample t-test Which assumption does a data analyst have to make when performing ANOVA on a dataset? There are just two parameters that are being estimated. The error terms follow a normal probability distribution. The parameters are additive. The explanatory variable is continuous. - ANSWERSThe error terms follow a normal probability distribution. Which two assumptions are made when the linear regression model is used? Choose 2 answers Critical value is based on Fisher's exact test. Error terms are independent and identically distributed. Variances are not equal. Parameters β 0, β 1, and σ 2 are constant. - ANSWERSError terms are independent and identically distributed. Parameters β 0, β 1, and σ 2 are constant. Which assumption is required to perform a two-sample t-test? Equal variance Large sample size Small sum of residuals Equal mean - ANSWERSEqual variance Given the following statistical model: y = 42 - 4.6 b Match each element of the model with its corresponding term. Answer options may be used more than once or not at all. Select your answers from the pull-down list. y Dependent variable Dependent variable 42 Intercept Intercept -4.6 Slope Slope b Independent variable Independent variable - ANSWERSy Dependent variable Dependent variable 42 Intercept Intercept -4.6 Slope Slope b Independent variable Independent variable Given the following generalized two-sample t-test equation: yi ,j = µi + εi ,j Classify each element in the equation. Answer options may be used more than once or not at all. Select your answers from the pull-down list. - ANSWERSyi ,j Observed value Observed value µi Mean response Mean response εi ,j Error term Error term Given the following linear model: y i = β 0 + β 1 xi + ε i Classify each element correctly. Answer options may be used more than once or not at all. Select your answer from the pull-down list. - ANSWERSy i Response variable Response variable β 0 + β 1 xi Mean response Mean response xi Explanatory variable Explanatory variable A study comparing graduating cumulative GPAs from students with two different majors is conducted to study the effect of each major on academic achievement. From the list of all graduating students in both majors, a random sample of 30 students from Major One and 30 students from Major Two are selected. The researcher decides to use an ANOVA test for this study. What will the researcher need to calculate? Sample size and sample mean Group means and standard deviations Population mean and standard deviation Percentage of the population sampled and population mean - ANSWERSGroup means and standard deviations A data analyst is studying the relationship between gender and marriage using the result below: T = test: Paired two sample for means Married Gender Mean 0.48 0.64 Variance 0.26 0.24 Observations 25 25 Pearson correlation 0.220176 Hypothesized mean difference 0 df 24 T stat -1.28103 Confidence level 0.95 P (T=t) one-tail 0.106213 t critical one-tail 1.710882 P (T=t) two-tail 0.212425 t critical two-tail 2.063899 Given a confidence level of 95%, what can be concluded? There is no significant difference of mean between these two groups given the t-values. There is a significant difference of mean between these two group as our null hypothesis is µ 1 - µ 2 = 0. There is a significant difference of mean between these two groups as Pearson correlation is positive. There is a significant difference of mean between these two group as our alternative hypothesis is µ 1 µ 2. - ANSWERSThere is no significant difference of mean between these two groups given the t-values. A junior data analyst intern is using linear regression to predict climate change. Given the following model: GAT ~ 0 + 0.2 OR + 0.1 GOT + 0.4 EAPG + 0.05 (EAPG)(OR) Given the following values: • OR = 10 • GOT = 5 • EAPG = 4 What is the correct result? 0.05 0.61 1.0 6.1 - ANSWERS6.1 From hospital records, the following values for the named components are obtained: Treatment Control Average birth weight of infant(g) SD 420 425 N 75 75 Birth weight is assumed to be normally distributed. The average birth weights in the two groups are tested using an independent two group t-test. H 0 is that there is no difference in the birth weight between the treatment and control groups with α = 0.05. Which formula can be used to solve the problem and show that the birth weight is significantly different? t = =5.07 t = = 1.39 t = = 43.93 t = = 12.04 - ANSWERSt = =5.07 A data analyst is doing an analysis using t-tests and gets the following output: t -stat: 2.8 p-value: .006 Critical value: 1.2 Which conclusion can be drawn? Accept the null hypothesis. The critical value is too high. Reject the null hypothesis. The two population means are similar. - ANSWERSReject the null hypothesis