Inference for Slope

Fast food is often considered unhealthy because of its high content of both fat and calories. But are the two related? The fat and calorie contents of several brands of burgers were analyze for their association between fat and calorie content. What is the name of inference use to determine if a relationship exists between these two variables?

• Z-test for a proportion

• T-test for a mean

• T-test for the slope of a regression line

• Chi square test of independence

• Z-test for a difference between two proportions

Tags

CCSS.8.SP.A.3

Joaquin believes that increasing his walking speed will increase his pulse rate. In an attempt to model this relationship, Joaquin records his pulse rate, in beats per minute (bpm), while walking at each of ten different speeds, in miles per hour (mph). A regression computer output is shown above. Provided that the assumptions for regression inference are satisfied, which of the following provides a 95 percent confidence interval pulse rate from walking speed?

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Tags

CCSS.HSS.IC.B.4

Joaquin believes that increasing his walking speed will increase his pulse rate. In an attempt to model this relationship, Joaquin records his pulse rate, in beats per minute (bpm), while walking at each of ten different speeds, in miles per hour (mph). A regression computer output is shown above. Provided that the assumptions for regression inference are satisfied, what can you conclude about the relationship between the walking speed and the pulse rate of Joaquin?

• Since the p-value is greater than any reasonable significance level, there is significant evidence of a linear relationship between the Joaquin’s walking speed and his pulse rate.

• Since the p-value is less than any reasonable significance level, there is insignificant evidence of a linear relationship between the Joaquin’s walking speed and his pulse rate

• Since the p-value is less than any reasonable significance level, there is significant evidence of a linear relationship between the Joaquin’s walking speed and his pulse rate.

• Since the p-value is less than any reasonable significance level, no linear relationship exists between the Joaquin’s walking speed and his pulse rate.

There is a general concern about blood sugar and brain shrinkage. An investigation of the relationship between blood sugar levels and brain shrinkage for 22 observations are shown in the table above. Assuming the conditions for inference are met, calculate the Margin of Error for the slope of the regression line for brain shrinkage on blood sugar levels using 90% confidence.

• 0.1201

• 0.1259

• 10.1233

• 10.6127

Tags

CCSS.HSS.IC.B.4

Information about the Size (in square feet) of 18 homes in Dallas, Texas, and the city’s assessed Value of those homes was collected and analyzed. Any inference about the regression of these two variable would use a degree of freedom of?

• 15

• 16

• 17

• 18

Tags

CCSS.8.SP.A.3

A researcher is conducting a study of charitable donations by surveying a simple random sample of households in a certain city. The researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. Let p represent the proportion of all households in the city that gave a charitable donation in the past year. Which of the following are appropriate hypotheses for the researcher?

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An agronomist is an expert in soil management and crop production. A certain state hires an agronomist to investigate whether there is a linear relationship between a wheat stalk’s height and the yield of wheat. The agronomist collected data and used the data to test the claim that there is a linear relationship at a significance level of α=0.05.

The agronomist tested the following hypotheses:

H0: β=0

Ha:β≠0

The test yielded a p-value of 0.25. Which of the following is a correct conclusion about the claim?

• The null hypothesis is rejected because 0.25>0.05. There is sufficient evidence to suggest that there is a linear relationship between a wheat stalk’s height and its yield.

• The null hypothesis is not rejected because 0.25>0.05. There is sufficient evidence to suggest that there is a linear relationship between a wheat stalk’s height and its yield.

• The null hypothesis is rejected because 0.25>0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk’s height and its yield.

• The null hypothesis is not rejected because 0.25>0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk’s height and its yield.

• The null hypothesis is accepted because 0.25>0.05. There is sufficient evidence to suggest that there is not a linear relationship between a wheat stalk’s height and its yield.

In the last question, the alternate hypothesis was ≠ and the p-value was 0.25.

If the alternate had been > instead of ≠, what would the p-value be?

• 0.125

• 0.25

• 0.50

• Impossible to say

A baseball enthusiast carried out a simple linear regression to investigate whether there is a linear relationship between the number of runs scored by a player and the number of times the player was intentionally walked. Computer output from the regression analysis is shown.

Let β represent the slope of the population regression line used to predict the number of runs scored from the number of intentional walks in the population of baseball players. A t-test for a slope of a regression line was conducted for the following hypotheses.

H0:β=0

Ha:β≠0

What is the appropriate test statistic for the test?

• t = 16/2.073

• t = 16/0.037

• t = 0.50/0.037

• t = 0.50/2.073

• t = 0.50/0.63