STATISTICS

ANOVA, ANCOVA, REGRESSION

Directions: Answer the following questions inside the picture and choose the correct answer. Explain why it is the correct answer. All the details for the question is indicated in the picture for each number.

1.

Three strains of rats were studied under two environmental conditions for their performance in a maze test. The error scores for the 48 rats were recorded as follows: Environment Strain Bright Mixed Free Dull 28 12 33 83 101 22 94 23 36 14 33 25 56 10 41 76 122 36 83 86 22 58 Restricted 35 72 23 32 60 89 136 48 120 93 35 126 38 25 153 31 83 110 64 91 128 19 99 118 87 140 At 0.01 level of significance, which of the following null hypothesis/hypotheses is/are rejected? I. There is no difference in error scores for different environment. II. There is no difference in error scores for different strains. Ill. The environments and strains of rats do not interact. a. I only b. II only c. Both I and II d. All of the above.A researcher wishes to see if the total number of infections that occurred in three groups of randomly selected hospitals is the same. The data are shown in the table. Group A Group B Group C 557 476 105 315 232 110 920 80 167 178 116 155 At ax = 0.05, is there enough evidence to reject the claim that the number of infections in the three groups of hospitals is the same? a. Since the computed value of 5.346 is less than the tabulated value of 5.991, there is no enough evidence to reject the claim that there is no difference in the number of infections in the groups of hospitals. b. Since the computed value of 5.991 is greater than the tabulated value of 5.346, there is enough evidence to reject the claim that there is no difference in the number of infections in the groups of hospitals. c. Since the computed value of 5.346 is less than the tabulated value of 5.991, there is enough evidence to reject the claim that there is no difference in the number of infections in the groups of hospitals. d. Since the computed value of 5.991 is less than the tabulated value of 5.346, there is no enough evidence to reject the claim that there is no difference in the number of infections in the groups of hospitals.Suppose that we want to build a model that predicts the group membership of a hurricane, either tropical (0) or non-tropical (1) based on the latitude of formation of the hurricane. The response variable is the binary variable Type . new (type of hurricane) and the predictor variable is FirstLat (First Latitude). Using R, we build a model by applying the gim ( ) function. For the logistic regression model, we specify family = "binomial". The data is available at https://userpage.fu-berlin.de/soga 200/2010 data sets hurricanes.xlax . The R code is Iset up filename my . filename 0.05 implying that the distribution of the data is significantly different from the normal distribution. b. The p-value >0.05 implying that the distribution of the data is significantly different from the non-normal distribution. c. The p-value > 0.05 implying that the distribution of the data is not significantly different from the normal distribution. d. The p-value >0.05 implying that the distribution of the data is not significantly different from the non-normal distribution.Friedman test is used to assess whether there are any statistically significant differences between the distributions of three or more paired groups. It's recommended when the normality assumptions of the one-way repeated measures ANOVA test is not met or when the dependent variable is measured on an ordinal scale. Using R for data analysis, we'll use the self esteem score dataset measured over three time points. The data is available in the datarium package. At 0.05 level of significance, test whether the self esteem score was statistically significantly different at the different time points during the diet. R code and its output is given below. R code and its output data ("selfesteem", package = "dacarium") head (selfesteem, 3) #1 / A tibble: 3 x 4 id 1 4.01 5.18 7.11 1 2 2 2.56 6.91 6.31 3.24 4.44 9.78 selfesteem 4 gather (key = "cime", value - "score", t1, t2, :3) 121 convert_as_factor (id, time) head (selfesteem, 3) # A tibble: 3 x 3 id time score 4 get_summary_stats (score, type . "common") Of A tibble: 3 x 11 time variable min max median iqr mean ad ## 1 t1 score 10 2.05 4.00 3.21 0.571 3.14 0.552 0.174 0.395 2 02 score 10 3.91 6.91 4.60 0.89 4.93 0. 863 0.273 0.617 score 10 6.31 9.78 7.46 1.74 7.64 1.14 0.361 0.817 res. fried 1 friedman_vest (score - time lid) res. fried ## # A cibble: 1 x 6 .Y. n statistic df p method fi * ## 1 score 10 18.2 2 0.000112 Friedman test Which of the following is the correct of the result of the data analysis using R? I The self esteem score was not statistically significantly different at the different time points during the diet. II. The self esteem score was statistically significantly different at the same time points during the diet. III. The self esteem score was statistically significantly different at the different time points during the diet. a I only b. II only c. Both I and II d. III only