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MATH1203 Graded HW 5 Spring 2021

We’ve wrapped this semester up by looking at associations between categorical variables and between quantitative variables. The goal of this assignment is to better understand these relationships by using StatCrunch to:

· Conduct Chi-squared tests of Independence

· Find and interpret the Odds Ratio for a 2x2 contingency table

· Create scatter plots of data

· Find the prediction equation

· Find and interpret and .

This HW also has an Extra Credit component.

1. In December 2019, a novel coronavirus (later designated COVID-19) was identified that would soon spread around the world. An existing drug called Remdesivir was identified early on as a potential treatment against the symptoms of COVID-19, which include severe respiratory infections. In the spring of 2020, a clinical trial assessed the efficacy of Remdesivir versus a placebo treatment in terms of the recovery of patients infected and hospitalized with the COVID-19 virus. Here, we look at data from this trial concerning patients with severe COVID-19 (those that needed oxygen supply). Of 222 such patients randomly assigned to the Remdesivir treat-ment group, 177 recovered after 28 days. Of 199 such patients randomly as-signed to the placebo group, 128 recovered after 28 days. The contingency table below shows these results.

· (2pts) What is the explanatory variable? The response variable?

· (2pts) We will run a Chi-squared test for independence. State the null and alternative hypotheses.

· (4pts) Use StatCrunch the run the Chi-squared test. Be sure to include the expected frequencies and the odds ratio. Insert an image of the output.

· (3pts) State the value of the test statistic, the P-value, and the Odds ratio.

· (2pts) If , what should the conclusion of our test be?

· (3pts) Interpret the odds ratio. Be sure to mention the strength of the association.

2. The contingency table below cross-lists a student’s year in school and their math grade for a particular high school.

· (2pts) What is the explanatory variable? The response variable?

· (2pts) We will run a Chi-squared test for independence. State the null and alternative hypotheses.

· (4pts) Use StatCrunch the run the Chi-squared test. Be sure to include the expected frequencies. Insert an image of the output.

· (2pts) State the value of the test statistic & the degrees of freedom.

· (2pts) If , what should the conclusion of our test be?

3. Open the “Beer” data file that was posted with this assignment. Copy the data and paste it into StatCrunch.

· (2pts) Create a scatterplot of the data. Let “alcohol content” be your explanatory variable and “calories” be your response variable. Insert an image of the plot. Does the data appear to be linear?

· (3pts) Use StatCrunch to find the prediction line. State the equation; round the slope and -intercept to TWO decimal places.

· (2pts) Is the association positive or negative? How do you know?

· (3pts) State the value of . What does this tell you about the association?

· (3pts) State the value of . How do we interpret in this problem?

· (2pts) According to the regression equation, what would we expect the calorie count to be for a beer that has an alcohol content of 13%?

· (2pts) Insert an image of both output windows from your regression analysis.

4. (10pts) Consider the scatter plots below. Explain your answers to the following questions.

· Which plot is decidedly NOT linear?

· Which plot seems most likely to have a negative correlation?

· Which plot seems most likely to have a positive correlation?

· Which plot seems most likely to have a value of that is close to 1?

· Which plot seems most likely to have a value of that is close to 0?

A XXXXXXXXXXB.

C XXXXXXXXXXD.

EXTRA CREDIT:

I. “Gamma” is a measure of association that we didn’t address in Chapter 8. Look up gamma (online, in a textbook, etc).

· What type of variables is gamma used for? Be specific!

· Look back at question 2. Run the Chi-squared test again, but this time ask StatCrunch to calculate gamma. State the value it gives, rounded to THREE decimal places (just the value, not the standard error, etc.).

· What does gamma tell us about the association between these two variables in question 2? Explain completely.

II. Go back to question 3, and run the regression process again, but this time switch the variables.

· State the equation; round the slope and -intercept to FIVE decimal places.

· Verify that the regression line passes through the point . Explain how you found and .

·

· What do you notice about the association after switching the variables? Positive? Negative? What about and ? Do these results make sense to you? Why or why not? Explain your thoughts completely.

We’ve wrapped this semester up by looking at associations between categorical variables and between quantitative variables. The goal of this assignment is to better understand these relationships by using StatCrunch to:

· Conduct Chi-squared tests of Independence

· Find and interpret the Odds Ratio for a 2x2 contingency table

· Create scatter plots of data

· Find the prediction equation

· Find and interpret and .

This HW also has an Extra Credit component.

1. In December 2019, a novel coronavirus (later designated COVID-19) was identified that would soon spread around the world. An existing drug called Remdesivir was identified early on as a potential treatment against the symptoms of COVID-19, which include severe respiratory infections. In the spring of 2020, a clinical trial assessed the efficacy of Remdesivir versus a placebo treatment in terms of the recovery of patients infected and hospitalized with the COVID-19 virus. Here, we look at data from this trial concerning patients with severe COVID-19 (those that needed oxygen supply). Of 222 such patients randomly assigned to the Remdesivir treat-ment group, 177 recovered after 28 days. Of 199 such patients randomly as-signed to the placebo group, 128 recovered after 28 days. The contingency table below shows these results.

· (2pts) What is the explanatory variable? The response variable?

· (2pts) We will run a Chi-squared test for independence. State the null and alternative hypotheses.

· (4pts) Use StatCrunch the run the Chi-squared test. Be sure to include the expected frequencies and the odds ratio. Insert an image of the output.

· (3pts) State the value of the test statistic, the P-value, and the Odds ratio.

· (2pts) If , what should the conclusion of our test be?

· (3pts) Interpret the odds ratio. Be sure to mention the strength of the association.

2. The contingency table below cross-lists a student’s year in school and their math grade for a particular high school.

· (2pts) What is the explanatory variable? The response variable?

· (2pts) We will run a Chi-squared test for independence. State the null and alternative hypotheses.

· (4pts) Use StatCrunch the run the Chi-squared test. Be sure to include the expected frequencies. Insert an image of the output.

· (2pts) State the value of the test statistic & the degrees of freedom.

· (2pts) If , what should the conclusion of our test be?

3. Open the “Beer” data file that was posted with this assignment. Copy the data and paste it into StatCrunch.

· (2pts) Create a scatterplot of the data. Let “alcohol content” be your explanatory variable and “calories” be your response variable. Insert an image of the plot. Does the data appear to be linear?

· (3pts) Use StatCrunch to find the prediction line. State the equation; round the slope and -intercept to TWO decimal places.

· (2pts) Is the association positive or negative? How do you know?

· (3pts) State the value of . What does this tell you about the association?

· (3pts) State the value of . How do we interpret in this problem?

· (2pts) According to the regression equation, what would we expect the calorie count to be for a beer that has an alcohol content of 13%?

· (2pts) Insert an image of both output windows from your regression analysis.

4. (10pts) Consider the scatter plots below. Explain your answers to the following questions.

· Which plot is decidedly NOT linear?

· Which plot seems most likely to have a negative correlation?

· Which plot seems most likely to have a positive correlation?

· Which plot seems most likely to have a value of that is close to 1?

· Which plot seems most likely to have a value of that is close to 0?

A XXXXXXXXXXB.

C XXXXXXXXXXD.

EXTRA CREDIT:

I. “Gamma” is a measure of association that we didn’t address in Chapter 8. Look up gamma (online, in a textbook, etc).

· What type of variables is gamma used for? Be specific!

· Look back at question 2. Run the Chi-squared test again, but this time ask StatCrunch to calculate gamma. State the value it gives, rounded to THREE decimal places (just the value, not the standard error, etc.).

· What does gamma tell us about the association between these two variables in question 2? Explain completely.

II. Go back to question 3, and run the regression process again, but this time switch the variables.

· State the equation; round the slope and -intercept to FIVE decimal places.

· Verify that the regression line passes through the point . Explain how you found and .

·

· What do you notice about the association after switching the variables? Positive? Negative? What about and ? Do these results make sense to you? Why or why not? Explain your thoughts completely.

Answered 1 days AfterMay 09, 2021

Solution 1:

· The response variable is Recovery.

The explanatory variable is Treatment.

· The null hypothesis is that there is no association between the two variables treatment and...

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