Question Set 1: Pearson's

Data concerning lab assignment scores (out of 100 points) and final exam scores (out of 60 points) were collected from a random sample of World Campus STAT 200 students. Copy+ paste the data in the table below into a Minitab Express worksheet to answer the following questions.

Lab Assignments

Final Exam

92

60

86

48

99

59

92

52

100

60

98

57

86

55

95

55

81

44

98

60

78

48

100

55

85

51

90

53

85

45

99

59

78

45

93

58

A. Use the five-step hypothesis testing procedure given below to determine if there is evidence of a relationship between Lab Assignments and Final Exam in the population of all World Campus STAT 200 students. Use Pearson's r. All calculations should be conducted in Minitab Express. Don't forget to show how you checked all of the assumptions. [25 points]

Step 1: Check assumptions & write hypotheses

Step 2: Compute the test statistic

Step 3: Determine the p-value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a "real world" conclusion

B. Compute the coefficient of determination for the relationship between Lab Assignments and Final Exam. [10 points]

C. Interpret the coefficient of determination that you computed in part B. [10 points]

Question Set 2: Simple Linear Regression

This question set will use the Gentoo.csv file, which can be downloaded from the Canvas page where you downloaded this lab document. This is a subset of the Palmer Penguins dataset that we used in the last lesson. This file contains data collected from 123 Gentoo penguins from Biscoe Island. In this question set, we will be exploring the relationship between bill length and bill depth.

Artwork by @allison_horst

https://github.com/allisonhorst/palmerpenguins

A. Use the five-step hypothesis testing procedure to determine if bill_ depth_ mm can be used to predict bill_ length_ mm in the population of all Gentoo penguins. Don't forget to show how you checked all of the assumptions.[25 points]

Step 1: Check assumptions & write hypotheses

Step 2: Compute the test statistic

Step 3: Determine the p-value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a "real world" conclusion

B. The second penguin in this sample had a bill depth of 16.3 mm. Using the regression equation you constructed in part A, compute the predicted bill length for this penguin. [10 points]

C. The second penguin in this sample had an actual bill length of 50.0 mm. Using this value and the predicted value from part B, compute the residual for the first penguin in this sample. [10 points]

D. Interpret the residual you computed in part C. [10 points]