Researchers at Consumer Reports analyzed three types of hot dogs, namely beef, p
ID: 3240006 • Letter: R
Question
Researchers at Consumer Reports analyzed three types of hot dogs, namely beef, poultry, and meat (mostly pork and beef, but up to 15% poultry meat). For each of the 54 hot dogs analyzed, they recorded the type, the calories, and the sodium level. Their data is available in the file DASL-HotDogNutrition.xlsx. Use this data file to answer the remaining questions.
Link to data set
https://drive.google.com/open?id=0B4XQhcmrtmtPTldFYlgtOUtTeWc
Let's examine the calories first. Construct Q-Q plots of the calories for each of the three types of hot dogs, and compare the variances to determine if the assumptions to use ANOVA have been met.
Question 12 options:
The assumptions have been met. It's safe to assume each group comes from a normally distributed population (from the Q-Q plots), and we can also assume that the variances are equal.
The assumptions have not been met. While it is safe to assume each group comes from a normally distributed population, we cannot assume that the variances are equal.
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, but we can assume that the variances are equal.
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, and we cannot assume that the variances are equal.
Run an ANOVA test to determine if the mean number of calories is the same for all three types of hot dogs. You should find that the degrees of freedom are 2 and 51, that F=16.074, and that P=.000 with a level of significance equal to 0.05. What conclusion can you draw?
Question 13 options:
We have sufficient evidence to claim that all three hot dog types have the same mean number of calories.
We do not have sufficient evidence to reject the claim that all three hot dog types have the same mean number of calories.
We have sufficient evidence to claim that all three hot dog types have a different mean number of calories.
We have sufficient evidence to claim that at least one of the hot dog types has a different mean number of calories than another type.
Now let's examine the sodium levels. Construct Q-Q plots of the sodium level for each of the three types of hot dogs. You should see that the Q-Q plot for poultry suggests a possible problem with the normality assumption. The smallest variance is 7180.75, and the largest is 10492.871. Have the assumptions been met to use use ANOVA?
Question 14 options:
The assumptions have been met. It's OK to assume each group comes from a normally distributed population (from the Q-Q plots), and we can also assume that the variances are equal.
The assumptions have not been met. While it is safe to assume each group comes from a normally distributed population, we cannot assume that the variances are equal.
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, but we can assume that the variances are equal.
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, and we cannot assume that the variances are equal.
Despite the possible problem with the Q-Q plot for poultry, you decide to use ANOVA to determine if the mean sodium levels are the same for all three groups. What is the P-value for this test?
What conclusion can you draw about the mean sodium levels of the three types of hotdogs? Use a level of significance of =0.05{"version":"1.1","math":"lpha = 0.05"}.
Question 16 options:
We have sufficient evidence to claim that all three hot dog types have the same mean sodium levels.
We do not have sufficient evidence to reject the claim that all three hot dog types have the same mean sodium levels.
We have sufficient evidence to claim that all three hot dog types have a different mean sodium levels.
We have sufficient evidence to claim that at least one of the hot dog types has a different mean sodium levels than another type.
The assumptions have been met. It's safe to assume each group comes from a normally distributed population (from the Q-Q plots), and we can also assume that the variances are equal.
The assumptions have not been met. While it is safe to assume each group comes from a normally distributed population, we cannot assume that the variances are equal.
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, but we can assume that the variances are equal.
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, and we cannot assume that the variances are equal.
Run an ANOVA test to determine if the mean number of calories is the same for all three types of hot dogs. You should find that the degrees of freedom are 2 and 51, that F=16.074, and that P=.000 with a level of significance equal to 0.05. What conclusion can you draw?
Question 13 options:
We have sufficient evidence to claim that all three hot dog types have the same mean number of calories.
We do not have sufficient evidence to reject the claim that all three hot dog types have the same mean number of calories.
We have sufficient evidence to claim that all three hot dog types have a different mean number of calories.
We have sufficient evidence to claim that at least one of the hot dog types has a different mean number of calories than another type.
Now let's examine the sodium levels. Construct Q-Q plots of the sodium level for each of the three types of hot dogs. You should see that the Q-Q plot for poultry suggests a possible problem with the normality assumption. The smallest variance is 7180.75, and the largest is 10492.871. Have the assumptions been met to use use ANOVA?
Question 14 options:
The assumptions have been met. It's OK to assume each group comes from a normally distributed population (from the Q-Q plots), and we can also assume that the variances are equal.
The assumptions have not been met. While it is safe to assume each group comes from a normally distributed population, we cannot assume that the variances are equal.
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, but we can assume that the variances are equal.
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, and we cannot assume that the variances are equal.
Despite the possible problem with the Q-Q plot for poultry, you decide to use ANOVA to determine if the mean sodium levels are the same for all three groups. What is the P-value for this test?
What conclusion can you draw about the mean sodium levels of the three types of hotdogs? Use a level of significance of =0.05{"version":"1.1","math":"lpha = 0.05"}.
Question 16 options:
We have sufficient evidence to claim that all three hot dog types have the same mean sodium levels.
We do not have sufficient evidence to reject the claim that all three hot dog types have the same mean sodium levels.
We have sufficient evidence to claim that all three hot dog types have a different mean sodium levels.
We have sufficient evidence to claim that at least one of the hot dog types has a different mean sodium levels than another type.
Explanation / Answer
Answer:
Question 12 options:
The assumptions have been met. It's safe to assume each group comes from a normally distributed population (from the Q-Q plots), and we can also assume that the variances are equal.
Run an ANOVA test to determine if the mean number of calories is the same for all three types of hot dogs. You should find that the degrees of freedom are 2 and 51, that F=16.074, and that P=.000 with a level of significance equal to 0.05. What conclusion can you draw?
Question 13 options:
We have sufficient evidence to claim that at least one of the hot dog types has a different mean number of calories than another type.
Now let's examine the sodium levels. Construct Q-Q plots of the sodium level for each of the three types of hot dogs. You should see that the Q-Q plot for poultry suggests a possible problem with the normality assumption. The smallest variance is 7180.75, and the largest is 10492.871. Have the assumptions been met to use use ANOVA?
Question 14 options:
The assumptions have not been met. It is not safe to assume each group comes from a normally distributed population, but we can assume that the variances are equal.
Despite the possible problem with the Q-Q plot for poultry, you decide to use ANOVA to determine if the mean sodium levels are the same for all three groups. What is the P-value for this test?
What conclusion can you draw about the mean sodium levels of the three types of hotdogs? Use a level of significance of =0.05{"version":"1.1","math":"lpha = 0.05"}.
Question 16 options:
We do not have sufficient evidence to reject the claim that all three hot dog types have the same mean sodium levels.
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