Question

More than 200,000 people worldwide take the GMAT examination each year as they apply for MBA programs. Their scores vary normally with mean about u= 525 and standard deviation about sigma= 100. One hundred students go through a rigorous training program designed to raise their GMAT scores. Test the hypotheses
H sub 0: u= 525
H sub A: u > 525
in each of the following situations:

a) The students' score is x = 541.4. Is this result significant at the 5% level?
b) The average score is x = 541.5. Is this result significant at the 5% level?
c) What conclusions may you draw by comparing the answers to parts a and b?

Answer 1

@jim_thompson5910 can you help please

Answer 2

what do you have so far?

Answer 3

A) z=(x-u)/(SD/sqrt(n))
z=(541.4-525)/100sqrt(100))
z=1.64
look up z=1.64 to find .4495
.5+.4495=.9495
since .9495<.95 we cannot reject null hypothesis

Answer 4

The alternate hypothesis is mu > 525

so this is a right tailed test

Answer 5

yes

Answer 6

what is P(Z > 1.64) equal to?

Answer 7

0.0505?

Answer 8

correct

Answer 9

b) The average score is x = 541.5. Is this result significant at the 5% level?

since

\[\Large P(Z > 1.64) = P(X > 541.5) \approx 0.0505\]

this means (p-value) > alpha where alpha = 0.05 in this case.

Because (p-value) > alpha is true, we fail to reject the null. Because the p value isn't really small, it's not statistically significant

Answer 10

okay so thats it for b? moving to c now?

Answer 11

yes you just need to do a and c

Answer 12

the work you have applies to part b

Answer 13

a) P{X>541.4}=P{Z>z}, z=(541.4-525)/100=0.164; P{}=0.44

Answer 14

i'm getting

p-value = 0.4349

but p-value = 0.44 works too

Answer 15

so for part a) we're failing to reject the null and the result is not statistically significant

Answer 16

yes

Answer 17

what conclusions can we draw?

Answer 18

that the null is correct, Their scores vary normally with mean approx 525 (with sd 100) not greater?

Answer 19

we haven't proven the null to be correct. We just can't reject it based on this evidence

Answer 20

so fix that to say *we don't have the evidence to prove the null is correct, so from what we have their scores typically vary with mean approx 525 not greater

Answer 21

the p values were larger than alpha = 0.05 which is why we fail to reject the null

failing to reject the null is not the same as proving the null is 100% true

Answer 22

but in a way, it's like concluding the null is true

Answer 23

okay so this is what I have for my answer:
A) P = 44, we're failing to reject the null and the result is not statistically significant
B) P(Z>1.64)=P(X>541.5) = 0.0505 we fail to reject the null. Because the p value isn't really small, it's not statistically significant
C) we don't have the evidence to prove the null is correct, so from what we have their scores typically vary with mean approx 525 not greater

Answer 24

P = 44 is not the pvalue for a

Answer 25

also, make sure to state the answer in your own words

Answer 26

.44* and yes i will transpose it when writing it down

Answer 27

? is that good @jim_thompson5910

Answer 28

I don't agree with what you wrote for c

Answer 29

the p values were larger than alpha = 0.05 which is why we fail to reject the null

failing to reject the null is not the same as proving the null is 100% true (but in a way, it's like concluding the null is true)

Answer 30

so all we would say was that we fail to reject the null simply because there is no evidence?

Answer 31

er not enough evidence to prove it wrong

Answer 32

so we can say something like

we fail to reject the null which means we have no choice but to accept that the mean score is 525

Answer 33

more stats testing would have to be done

Answer 34

oh okay got it

Answer 35

thank you! @jim_thompson5910

Answer 36

you're welcome