Hypothesis Testing 1. Harris (2020) tested levels of well-being in subjects with chronic anxiety undergoing brief therapy with mild psychedelics three months before and again three months after the administration of a single session of therapy. The well- being scores for the 16 subjects are listed in the "Before" and "After" columns in the Table below: Well-Being Scores Subject Before After A 125 133 B 96 126 115 115 108 119 93 124 F 98 109 G 95 72 H 120 104 107 113 126 118 K 102 121 L 116 115 M 80 94 105 87 123 121 110 118 Use the data provided in the table to test whether well-being changed significantly from immediately before to 3 months after the session. Set alpha at .05. a) Write a null and alternative hypothesis b) Determine the critical value and draw the comparison distribution with the rejection region(s) indicated c) Compute the relevant statistic

A researcher is interested in investigating the relationship between sugar consumption and weight gain for high school students. 15 volunteers were randomly assigned to one of two groups. The first group contained 6 volunteers who were put on a low sugar diet. The second group consisting of the remaining 9 volunteers was put on a diet with sugar constituting approximately 15% of their diet. After 8 weeks, the change in weight was recorded for each of the volunteers. Question: What is the response variable? What study principle was used in this study and what kind of study is this?

You are interested in investigating the efficacy of a new pain medication and design an experiment measuring pain levels before and after the administration of a new medication. You recruit 9 people to participate in your study and bring the same 9 participants in for two separate sessions. Here is the raw data: Pair Number Placebo Pain Score Pain Medication Pain Score 1 2 4 5 6 7 8 9 5 7 10 5 8 7 8 6 8 QUESTION 20 5 5 8 4 4 3 5 3 2 Use the t-test handout printout provided to calculate the t- statistic. What is the t-test statistic value? Round to the nearest tenth. What conclusion would you make on the above data, based on the t-value you calculated and the critical value of t? O You accept the null hypothesis because the t-value you calculated is inside the bounds of the critical t-value O You reject the null hypothesis because the t-value you calculated is inside the bounds of the critical t-value O You reject the null hypothesis because the t-value you calculated is outside the…

Johnson and Leone describe an experiment to investigate the warping of copper plates. The two factors studied were temperature and the copper content of the plates. The response variable was a measure of the amount of warping. The data are as follows: Temperature (°C) 50 75 100 Copper Content (%) 40 60 80 100 17 20 12 9 16 12 21 17 21 16 24 21 18 13 18 21 ZZFEHERRE 23 22 27 17 27 31 30 23 29 31 12 25 23 23 28 22 125 Source: Applied Statistics and Probability for Engineers, 6th Edition, Douglas, C. Montgomery & George, C. Runger. 1. Draw and interpret the interaction plot. ii. Is there any significant interaction between the factors? Use a = 0.05. ii. Can your interpretation in (i) be validated in (ii)? Twelve plants are randomly

You are given the following data, where X1X1 (final percentage in math class) and X2X2 (number of absences) are used to predict YY (standardized math test score in fifth grade):  YY X1X1 X2X2 375 88 3 480 98 0 310 61 5 450 89 1 345 70 3 410 72 1 465 92 2 350 70 3 370 75 4 390 80 1 420 80 2 350 78 3 415 95 2 Determine the following multiple regression values.Report intercept and slopes for regression equation accurate to 3 decimal places:     Intercept:   a=      Partial slope X1X1:   b1=      Partial slope X2X2:   b2=  Report sum of squares accurate to 3 decimal places:      SSreg=      SSTotal= Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places):     F-ratio =      P-value = Report the variance of the residuals accurate to 3 decimal places:     MSres= Report the results for the hypothesis test for the significance of the partial slope for number of absences…