1. Assuming a normal population distribution of X with population mean = 40 and population variance = 100, what is the mean of the sampling distribution of the mean and standard error of the mean using a sample size of 25?Mean = __________ Standard Error of the Mean = __________2. Calculate the 95% Confidence interval around a sample mean of 50, based on a sample N = 26 with a sx (standard deviation) = 10 3. An instructor gives the same final exam every year. She knows that the μ = 79 but the population variance is unknown. She thinks that her current class is advanced, and will do better than past classes (have a higher mean). The class consists of 25 students, and their final exam class mean was 87 with a variance estimate of 400. Assume that the parametric assumptions are NOT violated. Did her class do statistically better than previous classes? Conduct an appropriate statistical test using α = .05. Write your answer using the 8 steps of hypothesis testing.Questions 4 & 5 are attached in the images **Research Study on Reaction Times**A researcher conducted a study to investigate whether individuals have better reaction times depending on whether the test is administered in the morning or the afternoon. Sixteen participants were randomly assigned to complete the same reaction time test either in the morning or afternoon. Lower scores indicated faster reaction times. Due to the violation of parametric test assumptions, an appropriate statistical test using an alpha of 0.05 was required, following eight hypothesis testing steps.**Data Table**| Individual | Morning (X1) | R1 | X1² | Individual | Afternoon (X2) | R2 | X2² | D | Ranks | D² | ± ||------------|--------------|----|------|------------|----------------|----|------|----|------|-----|----|| 1 | 79 | | 6241 | 9 | 91 | | 8281 | -12 | | 144 | || 2 | 88 | | 7744 | 10 | 92 | | 8464 | -4 | | 16 | || 3 | 95 | | 9025 | 11 | 87 | | 7569 | 8 | | 64 | || 4 | 78 | | 6084 | 12 | 87 | | 7569 | -9 | | 81 | || 5 | 81 | | 6561 | 13 | 94 | | 8836 | -13 | | 169 | || 6 | 83 | | 6889 | 14 | 86 | | 7396 | -3 | | 9 | || 7 | 80 | | 6400 | 15 | 82 | | 6724 | -2 | | 4 | || 8 | 84 | | 7056 | 16 | 93 | | 8649 | -9 | | 81 | |**Totals & Means**- **Total Morning Scores:** 668 Dr. Phil conducted a study to determine if mothers give more hugs to their children than fathers do. He used 8 married couples and asked each parent to report the number of hugs given to their children over two weeks. The data collected assumes parametric assumptions were not violated. A statistical test is to be conducted with an alpha level of 0.05, following the eight steps of hypothesis testing.### Table OverviewThe table consists of the following columns:- **Pair**: Number assigned to each couple.- **Mother Hugs (X1)**: Number of hugs reported by the mother.- **R1**: Not specified (context needed).- **X1²**: Square of the number of hugs by the mother.- **Father Hugs (X2)**: Number of hugs reported by the father.- **R2**: Not specified (context needed).- **X2²**: Square of the number of hugs by the father.- **D**: Difference (X1 - X2).- **Ranks**: Ranks assigned based on differences.- **D²**: Square of the difference.### Data Summary- Pairs 1 to 8 recorded both mother and father hugs. - **Total** number of hugs by mothers: 73- **Total** number of hugs by fathers: 91- **Overall mean** for mothers' hugs: 9.125- **Overall mean** for fathers' hugs: 11.375- **Sum of differences (D)**: -18- **Sum of squares of differences (D²)**: 100The table provides data necessary for statistical analysis, likely a paired sample t-test, to evaluate the hypothesis that there is a difference in the number of hugs given by mothers as compared to fathers.

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Answered: Assuming a normal population…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P