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Problems and Solutions The following solution for data analysis using r shows how r is used to find the t-test and other parameters based on two different types of data. It also involves testing hypotheses, making decisions, and explaining the reason behind every decision.

Data Before Therapy 11 12 12 9 15 13 7 6 10 11 8 7 14 12 13 9 13 12 10 10 13 14 10 8 8 9 12 14 8 11 10 12

after 32 16 18 26 18 11 17 21 11 14 22 20 13 24

Therapy 23 30 19 27 30 35 21 31 30 28 32 26 29 34 12 17

For this assignment, you are required to use the statistical program R. Round all numerical answers to two decimal places and p values to three. The assignment is comprised of two problems. Each problem requires you to calculate the appropriate t-test with R. statisticsassignmenthelp.com

A commonly held belief is that it is always beneficial to one's emotional health to vent one's feelings after a traumatic event. A study attempted to actually test this idea.

Researchers tested the Emotional Well Being scores of subjects who had experienced a traumatic event, before and after they received psychotherapy. Perform an appropriate ttest with R to see if there is a difference in the Emotional Well Being scores before and after the psychotherapy.

Finding the t-test and deciding on the hypotheses Here, the means, standard deviations, and t-tests for the two different sets of data are calculated. Conclusions on hypotheses on each are given, and the results are all explained. The pooled variance is also calculated.

Finding the mean and standard deviation for the first set of participants 1a) what is the Mean for the Before Therapy group?

Answer: 10.875

1b)) what is the Standard Deviation for the Before Therapy group?

Answer: 2.390955 statisticsassignmenthelp.com

1c) what is the Mean for the After Therapy group?

Answer: 10.5625 1d) what is the Standard Deviation for the After Therapy group?

Answer: 2.393568 Deciding on the appropriate test 1e) what type of t-test is required here?

Answer: paired sample t test Deciding on the hypothesis 1f) based on your findings; can we reject the null hypothesis? Report your findings using the format below, as demonstrated in lab. Be sure to clearly state the variables. If there is a significant difference, clarify which direction it is going.

Answer: We cannot reject the null hypothesis. There is not a significant difference in mean between before therapy and after therapy. t(15)= 0.628 , p= 0.540 statisticsassignmenthelp.com

Problem 2 Researchers were interested in which of two methods were best for retention. They had all subjects read a chapter in a textbook. Then, one group of subjects ('Study') was encouraged to study the material for 60 minutes. The other group of subjects (‘Quiz’) was not allowed to study, but was actually given a 60 minute quiz on the material. Then, all subjects were required to complete a final test on the material. Perform an appropriate t-test on the final test scores with R to see if there is a difference in performance between the Study and Quiz groups Finding the mean and standard deviation for the second set of participants

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2a) what is the Mean for the Study group?

Answer: 18.7857 2b) What is the Standard Deviation for the Study group?

Answer: 5.950806 2c) What is the Mean for the Quiz group?

Answer: 26.5 2d) what is the Standard Deviation for the Quiz group?

Answer: 6.449806 Deciding on the appropriate test 2e) what type of t-test is required here?

Answer: Independent two sample t test

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Deciding on the hypothesis 2f) based on your findings; can we reject the null hypothesis? Report your findings using the format below. Be sure to clearly state the variables. If there is a significant difference, clarify which direction it is going.

Answer: We can reject the null hypothesis. There is a significant difference in the mean between before and after.

T ( 28) = -3.3873, p= 0.002 Finding the Pooled Variance 2g) Calculate the Pooled Variance () for this same t-test by hand. Hint: To save much time, use the Standard Deviations from the R output. Round to two decimals places. You do not have to show your calculations.

Pooled Variance () = 6.22 Q3 ############### statisticsassignmenthelp.com

> #Q1 > Assign3 <- read.delim("C:/Users/CSSC/Downloads/ Assign3.txt") > ETURN<-data.frame(Assign3) > mean(ETURN$BeforeTherapy,na.rm=TRUE ) [1] 10.875 > sd(ETURN$BeforeTherapy, na.rm = TRUE) [1] 2.390955 > mean(ETURN$AfterTherapy, na.rm= TRUE) [1] 10.5625 > sd(ETURN$AfterTherapy) [1] 2.393568 > t.test(ETURN$BeforeTherapy,ETURN$AfterTherapy,paired = TRUE, na.rm= TRUE)

Paired t-test

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data: ETURN$BeforeTherapy and ETURN$AfterTherapy t = 0.62795, df = 15, p-value = 0.5395 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.7482174 1.3732174 sample estimates: mean of the differences 0.3125 > #Q2 > mean(ETURN$Study,na.rm= TRUE) [1] 18.78571 > sd(ETURN$Study, na.rm=TRUE) [1] 5.950806 > mean(ETURN$Quiz, na.rm=TRUE) [1] 26.5 > sd(ETURN$Quiz, na.rm=TRUE) [1] 6.449806 > t.test(ETURN$Study,ETURN$Quiz, na.rm=TRUE) Welch Two Sample t-test statisticsassignmenthelp.com