Q. 89 Music and memory Refer to Exerci... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 10: Q. 89 (page 688)

Music and memory Refer to Exercise $87$ .
a. Construct and interpret a $99 %$ confidence interval for the true mean difference. If you already defined the parameter and checked conditions in Exercise $87$ , you don鈥檛 need to do them again here.
b. Explain how the confidence interval provides more information than the test in Exercise .

Short Answer

Expert verified

a. $99 %$ confidence interval for the true mean difference is $(0.2114, 2.9286)$ .

b. The confidence interval gives us the range of possible values for the true mean difference than the significance test.

Step by step solution

Part (a): Step 1: Given information

We need to Construct and interpret a $99 %$ confidence interval for the true mean difference.

Part (a): Step 2: Explanation

Given:

$n = S a m p l e s i z e = 30 {\overset{炉}{x}}_{d} = M e a n d i f f e r e n c e s = 1.57 s_{d} = S \tan d a r d d e v i a t i o n o f d i f f e r e n c e s = 2.70 c = c o n f i d e n c e l e v e l = 99 % = 0.99$

Now we will determine the confidence interval for the population mean difference.

Now at Degree of freedom

= 29 a n d c = 99 % t_{\frac{伪}{2}} = 2.756 T h e m a r g i n o f e r r o r i s : E = t_{\frac{伪}{2}} 脳 \frac{s_{d}}{\sqrt{n}} = 2.756 脳 \frac{2.70}{\sqrt{30}} 鈮� 1.3586 N o w t h e b o u n d a r i e s o f c o n f i d e n c e i n t e r v a l w i l l b e c o m e {\overset{炉}{x}}_{d} - E = 1.57 - 1.3586 = 0.2114 {\overset{炉}{x}}_{d} + E = 1.57 + 1.3586 = 2.9286 C o n f i d e n c e i n t e r v a l i s (0.2114, 2.9286)

Part (b): Step 1: Given information

We need to explain how the confidence interval provides more information than the test.

Part (b): Step 2: Explanation

The confidence interval gives us more information than the significance test because the confidence interval gives us a different range of possible values for true mean difference than the significance test because the significance test checks only one possible value for the true mean difference.