Suppose a sample of university students were asked the question. \"to hours, what was your phone screen time yesterday?" Some researchers wish to know if the average daily phone screen time of university students is significantly different from 4 hours. That is. they wish to test the hypotheses H.) :pzlversusHl 41,754, where p5 denotes the mean average daily phone screen time of university students in hours. Using the data collected. a onesample ttest was carried out with the following results: One Sample ttest data: screentime t = 8.05?6. df = 35, pvalue 1.?43e09 alternative hypothesis: true mean is not equal to 4 95 percent confidence interval: 4.464?1U 4.???T4? sample estimates: mean of x 4.621228 Furthermore, the effect size, Cohen's d. was calculated to be a! = 1.34. Does this result indicate the effect was negligible, small, medium, or large"? Select one: C) a. Negligible O b. Large Cl C. Small C) d. lvledium Suppose a group of 50 university students participated in a study which aimed to compare alertness levels before and after coffee consumption. In this study. the students were provided with a chart containing nine symbols. each coded with a number from i to 9. Then. the students were asked to perform the following coding task: one of the nine symbols. selected at random. appeared to the student. and they needed to correctly code this symbol to its associated number from i to 9. The time taken to complete this task was then recorded. Students completed this coding task both before and after coffee consumption. We wish to test the following hypotheses: Ho :pp 2 0 versus H1 : pig 75 0, where: . pip denotes the true mean difference in time taken to perform the task before coffee consumption compared with after coffee consumption Using the data collected. it was found that the average time taken to perform the task before coffee was 1.543'l seconds. while the average time taken to perform the task after coffee was 1.4U'l2 seconds. so that the estimated mean difference was 1.4012 l.5431 = 40.1419 seconds. A paired t-test was carried out with the following results: Paired ttest data: df$reaction.time by df$Group t = 0.9883. df = 49, p-value = 0.3279 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.4304152 0.1466280 sample estimates: mean of the differences -0.l418936 Answer the following questions. rounding your answers to three decimal places where relevant. (Note that a rounding tolerance has been built into the question. so that small discrepancies in mean differences due to rounding have been allowed for.) a. Wha is tre test statistic? b. Wha is tre degrees of freedom? 0. Wha is tre pvalue? d. Wha is tre sample mean of the difference? e. Wha' is tre LOWER bound of the condence interval (la. the lower number in the confdence interval range)? f. Wha' is the UPPER bound of the confidence interval lie. the higher number in the confdence interval range)? Suppose you are carrying out a paired ttest for a sample of data with sample size n = 25. and you wish to check for normality. Further suppose that, using the paired differences, you have carried out the ShapiroWilk test with the following results: ShapiroWilk normality test data: x W = 0.96169. pyalue = 0.4491 Using the results of the ShapiroWilk test alone, can normality be assumed? Select one: Q a. No, normality cannot be assumed C) b. Yes, normality can be assumed Suppose again that two new groups of 50 people have been randomly selected and asked their height in centimetres. The two groups are labelled "Group A" and "Group B". Further suppose that we wish to test the following hypotheses: Ho : M1 = /2 versus H1 : M1 7 /2, where: . M1 denotes the true average height of people in the Group A population . /2 denotes the true average height of people in the Group B population. Using the data collected, the following boxplots have been produced: 160 170 180 190 200 Height (cm) Group A Group B Using the information provided in this question, and with a significance level of a = 0.05, is there a statistically significant difference in average height between Group A and Group B? Select one: O a. There is not enough information provided in the question to draw a conclusion about statistical significance O b. Yes, there is a statistically significant difference O C. No, there is not a statistically significant differenceSuppose again that two new groups of 50 people have been randomly selected and asked their height in centimetres. The two groups are labelled "Group A" and \"Group B\". Further suppose that we wish to test the following hypotheses: Ho IP51 = #2 versus Ht I #1 75 #2: where: - p11 denotes the true average height of people in the Group x population . p12 denotes the true average height of people in the Group B population. Using the data collected. an independent samples ttest was carried out. The associated 95% confidence interval of the difference between ,u.1 and p32 is (6.973. -l .29). Using the confidence interval provided. and with a signicance level of o: = 0.05, is there a statistically significant difference in average height between Group A and Group B? Select one: Q a. Yes. there is a statistically significant difference :3 b. No. there is not a statistically significant difference C1 c. There is not enough information provided in the question to draw a conclusion about statistical significance Suppose again that two new groups of 50 people have been randomly selected and asked their height in centimetres. The two groups are labelled "GroupA" and "Group 8". Further suppose that we wish to test the following hypotheses: Ho 1H1 = #2 VBFSUS H1 I #1 #2: where: - #1 denotes the true average height of people in the Group A population - M denotes the true average height of people in the Group B population. Using the data collected. an independent samples ttest was carried out. The associated p value is 0.007. Using the pvalue provided. and with a signicance level ofo: = 0.05. is there a statistically signicant difference in average height between Group A and Group B? Select one: C] a. There is not enough information provided in the question to draw a conclusion about statistical significance C1 b. No. there is not a statistically significant difference it c. Yes. there is a statistically significant difference Suppose again that two new groups of 50 people have been randomly selected and asked their height in centimetres. The two groups are labelled "Group A\" and \"Group B". Further suppose that we wish to test the following hypotheses: Ho rm = #2 rms H1 IP51 # #2, where: +- pil denotes the true average height of people in the Group A population . #2 denotes the true average height of people in the Group B population. Using the data collected. an independent samples ttest was carried out with the following results: Nelch Two Sample ttest data: df$Height by df$Group t = 1.B303, df = 85.126, pvalue = 0.0?0? alternative hypothesis: true difference in means between group Group A and gr 95 percent confidence interval: 6.5571595 0.2?ii?13 sample estimates: mean in group Group A mean in group Group B 1?3.8682 i??.0i12 Answer the following questions. rounding your answers to three decimal places where relevan;. a. What is tre test statistic? b. What is tre degrees of freedom? c. What is tre pvalue? d. What is tre sample mean for Group A? l e. What is the sample mean for Group B? I f. What is tre LOWER bound of the confidence interval (is. the lower number in the cc ndence interval range)? g. What is the UPPER bound of the confidence interval lie. the higher number in the confidence interval range)? Suppose again that two new groups of 50 people have been randomly selected and asked their height in centimetres. The two groups are labelled "Group A\" and "Group B\". Further suppose that we wish to test the following hypotheses: Ho IP51 = #2 versus H1 I #1 #2; where: - #1 denotes the true average height of people in the Group A population - p2 denotes the true average height of people in the Group B population. The results ot the Levene's test are provided below: Levene's Test for Homogeneity of Variance (center = "mean") Df P value Pr(>F) group 1 0.4282 0.5144 98 Using the results of the Levenels test. complete the sentences below using the options from the drop-down menus provided: a. Based on the results of the Levene's test. equal variances e be assumed. b: Given the results of the Levene's test, we should use the version of the independent samples ttestthat assumes equalvariances. Suppose two groups of 50 people have been randomly selected and asked their height in centimetres. The two groups are labelled \"Group A" and \"Group B\". Further suppose that we wish to test the following hypotheses: H0 : p1 2 #2 versus H1 : p51 # p52, where: - #1 denotes the true average height of people in the Group A population - #2 denotes the true average height of people in the Group B population. The following information has been produced in order to check one of the assumptions: Group A Normal O-Q plot for Group a LO 3 W 2 "E d 9 5: E 0 OJ 2 \"a\". g D E {I} C) C, (n c:- Q P D lllI 160 1?0 130 2 -1 0 1 2 Height (cm) Theoretical Ouantiles Group B Normal Q-Q plot for Group E N a 0 d E i: a \" 3. E 99 a o :1 g g r\"? a g F a (D N '1 :1 r~ D lYllI ' 160 1?0 130 2 -1 0 1 2 Haghucm) Theomcalduanmes Sample size of Group A: 50 Sample size of Group B: 50 Shapiro-Wilk test for Group A: ShapiroWilk normality test data: df$Height[df$Group == \"Group A"] W = 0.96825. pvalue = 0.1963 Shapiro-Wilk test for Group B: ShapiroWilk normality test data: df$Height[df$Group == \"Group 8"] w = 0.97589. p-value = 0.3944 Which assumption can we check for using the above information\"? Choose the best answer from the options below: Select one: Q a. The data are numeric O b. Normality O c. Independence of observations Q d. Equality of variances Suppose two groups of 50 people have been randomly selected and asked their height in centimetres. The two groups are labelled "Group ll" and "Group B\". Further suppose that we wish to test the following hypotheses: H.) 3#1 2 p52 versus H1 : H1 #2, where: - ,ul denotes the true average height of people in the Group A population . pg denotes the true average height of people in the Group B population. The following information has been produced in order to check one of the assumptions: 1?!) 130 1H] Height (cm) 160 Group A Group B Standard deviation for Group A: ?.72 Standard deviation for Group B: 6.77 Levene's Test for Homogeneity of Variance (center = \"mean") Df P value Pr(>F) group 1 0.4858 0.48T5 98 Which assumption can we check for using the above information? Choose the best answer from the options below: Select one: Q a. Normality C1 b. Independence of observations 0 c. The data are numeric [:1 d. Equality of variances