# Stats: Correct or not?

• Nov 9th 2007, 12:04 PM
Nimmy
Stats: Correct or not?
Can someone check my work?

Q
1. A recent study found that, at most, 32% of people who have been in a plane crash have died. In a sample of 100 people who were in a plane crash, 38 died. Is the study statement believable?

Solution:

H(null): P= 0.32
H(alternative): P>0.32 Right tailed

P(hat): 0.38
P= 0.32
n= 100

Then you use the test statistic

z= P(hat)-P/Sqrt(pq/n)
z= 0.38-0.32/sqrt(0.32 x 0.68/100)~ 1.29

So I look for the area on the z score chart and it should be 0.90147. However since that's the area on the left side of the z score. So i must do 1-0.90147= .0985

.0985<0.05 so Reject H(null).....So the statement is believable right?
• Nov 9th 2007, 01:20 PM
galactus
What alpha level are you using?. You didn't say. I assumed .05

$\displaystyle H_{0}:p\leq{0.32}$(claim)
$\displaystyle H_{a}:p>0.32$

Test stat = 1.2862

critical value = 1.6449

p value = 0.0992

Do not reject the null hypothesis.

There is not enough evidence at the 5% level to reject the claim that at most 32% of plane crash victims die.

The claim is valid.

If you test at alpha = 0.1, then you can reject.
• Nov 9th 2007, 01:22 PM
CaptainBlack
Quote:

Originally Posted by Nimmy
Can someone check my work?

Q
1. A recent study found that, at most, 32% of people who have been in a plane crash have died. In a sample of 100 people who were in a plane crash, 38 died. Is the study statement believable?

Solution:

H(null): P= 0.32
H(alternative): P>0.32 Right tailed

P(hat): 0.38
P= 0.32
n= 100

Then you use the test statistic

z= P(hat)-P/Sqrt(pq/n)
z= 0.38-0.32/sqrt(0.32 x 0.68/100)~ 1.29

So I look for the area on the z score chart and it should be 0.90147. However since that's the area on the left side of the z score. So i must do 1-0.90147= .0985

.0985<0.05 so Reject H(null).....So the statement is believable right?

Assuming your arithmetic is right wha you have is:

0.0985>0.05 so we do not reject H(null) at the .....So the statement is believable in that we do not reject the hypothesis at this level.

RonL

RonL
• Nov 9th 2007, 01:38 PM
Nimmy
Quote:

Originally Posted by galactus
What alpha level are you using?. You didn't say. I assumed .05

$\displaystyle H_{0}:p\leq{0.32}$(claim)
$\displaystyle H_{a}:p>0.32$

Test stat = 1.2862

critical value = 1.6449

p value = 0.0992

Do not reject the null hypothesis.

There is not enough evidence at the 5% level to reject the claim that at most 32% of plane crash victims die.

The claim is valid.

If you test at alpha = 0.1, then you can reject.

Is that another way you can solve it? Is my work wrong? How did you get the critical value?
• Nov 9th 2007, 01:50 PM
Nimmy
Quote:

Originally Posted by CaptainBlack
Assuming your arithmetic is right wha you have is:

0.0985>0.05 so we do not reject H(null) at the .....So the statement is believable in that we do not reject the hypothesis at this level.

RonL

RonL

oh lol you right. I assume it was 0.5 instead of 0.05