3. Given the following information, complete the tree diagram for a two-stage experiment with three outcomes X, Y, and Z in the first stage, and two outcomes a and b in the second stage: Pr[X] = 1/2, Pr[Xa] = 1/8, Pr[Xb) = 3/8, Pr[a|Y] = 1/4, Pr[b|Y] = 3/4, Pr[Ya] = 1/24, Pr[Yb) = 1/8, Pr[Za] = 1/6 %3D
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- “A researcher wants to examine the effects of siblings on the amount of annual salary people earned when they are 35 years old. Salary data of three groups of 35-year olds were collected and are presented here. 4 participants with no sibling while growing up (n1 = 4): 50K, 51K, 49K, 50K. 5 participants with 1 to 2 siblings while growing up (n2 = 5): 55K, 56K, 54K, 58K, 52K. 4 participants with 3 and more siblings while growing up (n3 = 4): 60K, 60K, 70K, 50K. The researcher calculated: ∑x2 = 39747, G2/N = 39325, ∑T2/n = 39525.” Do the data indicate significant differences among the three groups of 35-year olds? Test at the alpha = .05 level. a. No, the calculated F value was not larger than the critical F value; results were not statistically significant and fail to reject the null hypothesis. b. Yes, the calculated F value was not larger than the critical F value; results were not statistically significant and fail to reject the null hypothesis. c. Yes,…The following data show the pattern of results that was obtained in a study by Liguori and Robinson (2001) examining how different levels of alcohol and caffeine consumption influenced response time in a simulated driving test. The means show the average response time in milliseconds for different combinations of alcohol and caffeine. Remember larger reaction time means someone is slower to respond. For these data, indicate which are true/false There is an interaction, caffeine has a larger impact on reaction times (makes people respond faster) when participants haven’t had alcohol) A. True B. False7) The following results are from data that were collected from a sample of Chicago Cubs baseball games. The dependent variable is ATTENDANCE, TEMP is a variable measuring the forecasted game-time temperature: WIN% is a variable measuring the winning percentage of the Cubs before the game is played, OPWIN% is a variable measuring the winning percentage of their opponent, WEEKEND is a dummy variable = 1 if the game is played on a weekend and = 0 if the game is played during a weekday, PROMOTION is a dummy variable = 1 if there is a promotion for the game (giving away something to those who attend the game) and = 0 if there is not a promotion, and WEEK*PROM is an interaction term equal to WEEKEND*PROMOTION. a) What is the predicted attendance if TEMP = 70, WIN% = 500, OPWIN% = 500, the game is played on a weekend and there is NO promotion? b) What is the predicted attendance if TEMP = 70, WIN% = 500, OPWIN% = 500, the game is played on a weekend and there is a promotion? c) Based on…
- To investigate the effect of price on toaster sales, a chain of department stores decided to raise the price of a certain brand of toaster in 20 randomly selected stores (Sample A) and to lower the price in 10 randomly selected stores (Sample B). Monthly revenue (number sales x sales price) from these toasters was recorded for each of the 30 stores. Results from the two samples are as follows: No. of stores Мean Std. Dev. Sample A Sample B $842 $817 $217 $202 20 10 If you considered these to be independent samples, what would be the pooled estimate of the standard deviation for revenue? Calculate a 95% confidence interval for the difference between (а) (b) the two means.2. Two modeling scouts are on the bus rating the attractiveness of their fellow passengers on a scale of one to five. When they were finished, they noticed that one of them had five scores with the maximum possible error, while the other had five scores with the minimum possible error. For both you and your friend give: a.) each of the five answers that were given; b.) calculate the appropriate measure of central tendency, and c.) calculate the appropriate measure of dispersion. Central Dispersion Anna Bill Carl Delia Ellen Tendency Max. Error Min. Error6. The following data are the weight gained in kgs of 15 dairy calves, grouped by cage, fed with 5 different brands of feed (T1, T2, T3, T4, T5) mixed with their feeds (kg). The experiment was conducted in RCBD. The calves are grouped into three cages as blocks. Treatment Blocks II T1 2.8 5.8 5.3 T2 2.7 3.6 3.5 T3 2.8 2.5 2.1 T4 3.2 3.8 3.5 T5 3.2 5.2 a. Coefficient of Variation (CV), b. Make a Decision 5323
- 1.3 A random set of boys and girls who formed part of a sociology experiment conducted at the University of Cape Town, are observed to respond differently to a specified situation. Their response rates are reflected in Table 1. Table 1: Response rates Response Type Females Males (Girls) 50% (Boys) Good 60% The experimental group of 50 kids, 20 boys and 30 girls aged between 6 and 10 years old, was exposed to these specified settings, and they were requested to describe their responses on a digital survey. A random response selected from the 50 kids was bad. Determine what the probability was that it was boy?A doctor is trying to decide if a patient has one of three diseases d1, d2, or d3. Two tests are to be carried out, each of which results in a positive (P) or a negative (N) outcome. There are four possible test patterns PP, PN, NP, and NN. National records have indicated that, for 10,000 people having one of these three diseases, the distribution of diseases, and test results are as shown below: Please find the image below What is the probability that a randomly selected patient has the 2nd disease d2? What is the probability that a randomly selected patient has a test result of NP? If a randomly selected patient gets a test result of NP, what is the probability that the patient has the third disease d3?. . 3 2 0 _1 A study was conducted to determine if taking a popularly advertised herbal supplement will result in weight loss in obese males. A random sample of clinically obese males was obtained. Each subject was weighed before taking the supplement and again after 60 days using the supplement. Subjects were told not to alter their diet in any way during the study period. The following table shows the observed results for the six subjects. ] Subject Before (B) After (A) D=B-A 1 2 164 172 166 154 -2 18 What is the 95% confidence interval for this matched pair test? (3.4, 15.9) (-1.57, 16.9) (1.57, -16.9) (-3.4, 15.9) 3 186 176 10 4 166 170 -4 5 6 174 178 160 168 14 10
- You also conducted a review of the research literature and found that similar studies examining the relationship between alcohol consumption and liver cancer found the following: Smithson et al. RR 3.3 (95% CI:1.95-5.20) Ribera et al. RR 2.1 (95% CI:1.17-3.33) Gonzalez et al. RR 2.75 (95% CI 2.26-3.45) Which one of Hill’s criteria does this illustrate? Explain.a) Three samples of five mice were randomly selected to be placed in a standard maze but with different door colours (red, green, black). The time (in seconds) required to complete the maze was recorded as in Table 1. Table 1: Time to Complete the Maze Color Time Red 9. 11 10 9 15 Green 20 21 23 17 Black 8 14 7 (i) Identify the dependent and independent variables. (ii) How many treatments involved in this study? (iii) How many replications for each treatment?Reggie is running his stats for a project he just finished. He had participants came in to the lab and gave them a drug treatment (either a control or an experimental compound) at different times during the day (morning, afternoon, and night). Each participant went through all off of the conditions. He ran an ANOVA and tested for the main effects and their interaction. Assuming that only the main effects (and not the interaction) came back significant, interpret his results (no need to include tests statistics).