1 7 points Consider the ST314 Summer Survey Data to compare

1. (7 points) Consider the ST314 Summer Survey Data to compare the reported number of close friends among those with or without a social networking profile. Review the boxplot and R software output.

a. (3 points) Compare the data visually and numerically by using the boxplot and summary statistics. Does there seem to be evidence of a difference between the average number of close friends between the two groups? Explain in context.

b. (2 points) The R output above is the results from performing two sample t test. In this test, I assumed the variances of the population were equal and therefore performed a “pooled t test”. Based on the p-value from the output, is there evidence that the average of close friends is different between the two groups?

c. (2 points) What is wrong with using this test and the assumption that the population variances are equal?

2. (21 points) Using the same data from part 1 answer the following questions to perform a Welch’s Two Sample t test to see if there evidence that the average of close friends is different between those with a profile and those without a profile. (Note: This is the test shown in the notes and page 357 of text. It does not assume equal variances.) Use a significance level of 0.05.

a. (2 points) State the null and alternative hypotheses.
b. (3 points) State and check the conditions for inference. (Note: If you find they are not met, state so and why. Then proceed)
c. (1 points) By hand, calculate the Satterwaite degrees of freedom. Show work.
d. (3 points) By hand using the summary statistics in part 1, calculate the t test statistic. Show work.
e. (1 points) State the appropriate p-value.
f. (3 points) By hand, calculate the 95% confidence interval for the difference between means among the two groups.
g. (3 points) Using the code from data sets and code, perform the two sample t test using R. Paste output here. Are the results from output the same as parts c – f?
h. (3 points) Answer the question of interest based on the R output in part g. Make a four part conclusion.
i. (2 points) Lastly, compare the results between the Welch’s Two sample t test (part g) and the “Pooled” Two Sample t test (part 1). How are the results different?

Please, lebal each answer with its question. For example:

1. A)

B)

2)

A)

B)

and so on.

Please answer all parts

thank you in advance

Solution