Question

11.4 #7

Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information.

x	0.328	0.270	0.340	0.248	0.367	0.269
y	3.2	7.8	4.0	8.6	3.1	11.1

(a) Find ?x, ?y, ?x², ?y², ?xy, and r. (Round r to three decimal places.)

?x =
?y =
?x2 =
?y2 =
?xy =
r =

(b) Use a 5% level of significance to test the claim that ? ? 0. (Round your answers to two decimal places.)

t =
critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ? differs from 0.Reject the null hypothesis, there is insufficient evidence that ? differs from 0.    Fail to reject the null hypothesis, there is insufficient evidence that ? differs from 0.Fail to reject the null hypothesis, there is sufficient evidence that ? differs from 0.

(c) Find S_e, a, and b. (Round your answers to four decimal places.)

Se =
a =
b =

(d) Find the predicted percentage ? of strikeouts for a player with an x = 0.34 batting average. (Round your answer to two decimal places.)
%

(e) Find an 80% confidence interval for y when x = 0.34. (Round your answers to two decimal places.)

lower limit	%
upper limit	%

(f) Use a 5% level of significance to test the claim that ? ? 0. (Round your answers to two decimal places.)

t =
critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ? differs from 0.Reject the null hypothesis, there is insufficient evidence that ? differs from 0.    Fail to reject the null hypothesis, there is insufficient evidence that ? differs from 0.Fail to reject the null hypothesis, there is sufficient evidence that ? differs from 0.

Answer 1

Hello.

I'm using excel to solve your question. If you want it solved in any other way, let me know in the comments and I'll suggest you to post a new question for (e) and (f) parts specifically mentioning to attempt only those parts.

(a)

(b)

, df = n - 2

Critcal t,

df = n - 2 = 4,

(c) Using Data -> Data Analysis -> Regression

Hence, SE = 1.7145, a = 25.1927, b = -62.2153

(d)

I hope this solves your doubt.

Do give a thumbs up if you find this helpful.