AP Statistics Question?

Question

I've been having a bit of trouble with this question. Perhaps if someone can help.

Sarah’s parents are concerned that she seems short for her age. Their dr. has 
recorded Sarah’s age and height on six consecutive office visits. These data were 
entered into a Minitab worksheet, and Sarah’s height was regressed on her age. 
Here is the computer output:

Predictor   Coef     St.dev      T-ratio   P
Constant   71.950  1.053       *          *
Age          0.3833   0.02041   *          *

s = 0.3873 R-sq = 98.9% R-sq(adj) = 98.9%

1) Suppose we want to conduct a test to determine whether Sarah’s age is useful in 
predicting her height. Write appropriate null and alternative hypotheses for such a 
test. State the assumption that you would check.

2) What is the equation of the least-squares regression line?

3) The t statistic for testing Ho has been left out. Use the output to find t.

4) How many degrees of freedom does t have?

5) Approximate the p-value.

6) Write your conclusions in plain language.

7) Construct a 95% confidence interval for the population regression slope.


Thanks in advance!! I will choose "Best Answer!"

BeeFree · Accepted Answer

Matt -


1) Suppose we want to conduct a test to determine whether Sarah’s age is useful in 
predicting her height. Write appropriate null and alternative hypotheses for such a 
test. State the assumption that you would check.

Ho: β = 0

Ha: β ≠ 0

2) What is the equation of the least-squares regression line?

y = a + bx = 71.950 + 0.3833(Age)


3) The t statistic for testing Ho has been left out. Use the output to find t.

t = b / (standard deviation of b) = 0.3833 / 0.02041 = 18.78

4) How many degrees of freedom does t have?

d.f. = 6 - 2 = 4 [this came from the text, not the computer output]

5) Approximate the p-value.

p-value = 0.00000237 [TI-84 calculator: tcdf(18.78,1000000,4)

6) Write your conclusions in plain language.

Since p is close to zero, there is significant evidence of a predictive linear relationship between height and age.

Note: R^2 = 98.9% which is really high and is telling you 98.9% of the variation in height is explained by age.

7) Construct a 95% confidence interval for the population regression slope.

At 95% and 4 d.f. , t = 2.776 (from t-tables or invT)

CI = b ± (t)(standard deviation of b)

= 0.3833 ± (2.776)(0.02041) = 0.3266 to 0.4400

Hope that helps

P.S. - A great review book for the AP Stats is "5 steps to a 5" by Duane C. Hinders. I use this to tutor AP Stats and it is the best book out there.

Anonymous · Answer

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AP Statistics Question?

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