Stat 12.1

To see if students with longer feet tend to be taller, a random sample of 25 students was selected from a large high school. For each student, x=foot length (cm) and y=height (cm) were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of computer output for this data. Which of the following is the equation for the least squares regression line for predicting height from foot length?

• predicted height = 10.2204 + 0.4117 (foot length)

• predicted height = 0.4117 + 3.0867 (foot length)

• predicted height = 91.9766 + 3.0867 (foot length)

• predicted height = 91.9766 + 6.47044 (foot length)

Tags

CCSS.HSS.ID.C.8

The slope, B1, of the population regression line describes (remember the sample was randomly selected)

• the average increase in foot length for students at this high school when height increases by 1 cm

• the average increase in height for students at this high school when foot length increases by 1 cm

• the average increase in foot length for students in the sample when height increases by 1 cm

• the average increase in height for students in the sample when foot length increases by 1 cm

Tags

CCSS.8.SP.A.3

Is there convincing evidence that height increases as foot length increases? To answer this question, test the hypotheses

• H0: B1=0 versus Ha: B1>0

• H0: B1=0 versus Ha: B1<0

• H0: B1=0 versus Ha: B1 does not equal 0

• H0: B1>0 versus Ha: B1=0

Which of the following is a 95% confidence interval for the population slope? Remember n=25.

• 3.0867+-0.4117

• 3.0867+-0.8518

• 3.0867+-0.8069

• 3.0867+-0.8497

Which of the following is the best interpretation of the value 0.4117 in the computer output?

• For each increase of 1 cm in foot length, the average height increases by about 0.4117 cm.

• When using this model to predict height, the predictions will typically be off by about 0.4117 cm.

• The linear relationship between foot length and height accounts for 41.17% of the variation in height.

• In repeated samples of size 25, the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about 0.4117.

Tags

CCSS.8.SP.A.3

Which of the following would have resulted in a violation of the conditions for inference?

• If the entire sample was selected from one classroom.

• If the sample size was 15 instead of 25.

• If the scatterplot of foot length and height did not show a perfectly linear relationship.

• Is the histogram of heights had an outlier.

Tags

CCSS.HSS.ID.B.6B