Question

answer please can simplify process

Two experimental diets, designed to add weight to malnourished adults in developing countries, are being tested. The following sample data for weight gain after 6-weeks on the diet (in kg) was obtained (assume normally distributed data): N4 = 8, mean = 5.80, S4 = 1.613 for Diet A and n2 = 9, mean = 7.27, 92 = 0.99 for Diet B. You use the pooled t-test to test whether Diet B is better than Diet A with respect to gaining weight. What is the p-value of the test given that the pooled standard deviation is 1.3179? O A. Between 0.025 and 0.05 B. Less than 0.01 C. Greater than 0.10 D. Between 0.05 and 0.10 E. Between 0.01 and 0.025

Answer 1

Solution:

The null and alternative hypothesis are

H0:  $url=https://latex.codecogs.com/gif.latex?%5Cmu&t=1596159474&ymreqid=f4764063-0d40-e2b0-1cde-f0004d012f00&sig=.AzmxtZ4aHIrLJH.sS7C3g--~D$₁ =  $url=https://latex.codecogs.com/gif.latex?%5Cmu&t=1596159474&ymreqid=f4764063-0d40-e2b0-1cde-f0004d012f00&sig=.AzmxtZ4aHIrLJH.sS7C3g--~D$₂ vs Ha : $url=https://latex.codecogs.com/gif.latex?%5Cmu&t=1596159474&ymreqid=f4764063-0d40-e2b0-1cde-f0004d012f00&sig=.AzmxtZ4aHIrLJH.sS7C3g--~D$ ₁ <   $url=https://latex.codecogs.com/gif.latex?%5Cmu&t=1596159474&ymreqid=f4764063-0d40-e2b0-1cde-f0004d012f00&sig=.AzmxtZ4aHIrLJH.sS7C3g--~D$₂

$url=https://latex.codecogs.com/gif.latex?s_%7Bp%7D&t=1596159474&ymreqid=f4764063-0d40-e2b0-1cde-f0004d012f00&sig=PCRbP8m3kDRHlwVEnpvifQ--~D$ denotes the pooled standard deviation.

$url=https://latex.codecogs.com/gif.latex?s_%7Bp%7D&t=1596159474&ymreqid=f4764063-0d40-e2b0-1cde-f0004d012f00&sig=PCRbP8m3kDRHlwVEnpvifQ--~D$ = 1.3179

The test statistic t is given by

t =

T1 T2 + ) 111 112

=  

5.80 -7.27 1.31792 * (G+

= -2.295

Test statistic t = -2.295

Now ,

d.f. = n₁ + n₂ - 2 = 8 + 9 - 2 = 15

< sign in Ha indicates that the test is "One tailed left sided"

Use t table .

See the column of d.f.

Go to 15 d.f.

In the row of 15 , see where the value 2.295 fits in between.

It fits between 2.131 and 2.602

See the corresponding alpha values at ONE tailed

0.025 and 0.01

So , range of p value is 0.01 to 0.025

Answer is

E. Between 0.01 < p-value < 0.025