# Hypothesis Testing

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#### benchiefjr

##### New Member
benchiefjr said:
I have a question

Teaching method A produces a mean score of 75 on a standard test. Teaching method B has been introduced, and the first sample of 19 students achieved a mean score of 79 with a standard deviation of 8. At 5% level of significance, test the claim that method B is better.

H0 : Mb <= Ma
H1 : Mb > Ma

I completely forgot how to do this type. I have a feeling if i see it done, I'll remember. Please help me!
I did this

X bar = 75
n = 19
std. dev. = 8

75-8/1.835 = 36.5 which is > 1.835

Fail to reject H0. There is a significant difference between the two means, therefore supporting the claim that method B is better than method A.

Is this right?

benchiefjr said:
Like this one :

An experiment is devised to study the variability of grading procedures among college professors. Two different professors are asked to grade the same set of 25 exam solutions and their grades have variances of 103.4 and 39.7, respectively. At the 0.05 siginificance level, test the claim that the professor's grading exhibits greater variance.

H0 : o1 <= o2
H1 : o1 > o2

The o is like the std. dev. symbol i believe. I just can't tell if this is the same as the other problem because it has to do with variances.
This one...DF = 24 alpha = .05

C.V. = 36.42

(24)(103.4)/39.7 = 62.5

62.5 > 36.42

Reject H0. The sample of 25 solutions comes from a distribution with a variance greater than 36.42.

Are these right, if not..please help! Also, if someone could do one of the other two, that'd be great because then i'd be finished.

#### JohnM

##### TS Contributor
Should be z=(79-75)/(8/sqrt(19)) = 2.179

Prob(z >= 2.179) = .0146 which is less than .05 (level of significance) and therefore we reject Ho, thereby concluding that method B is better than method A.

#### benchiefjr

##### New Member
was the other one right? And if so, can you PLEASE do one of the other two...i'd really appreciate it. I'm struggling badly on those two. I'm sorry if i'm being annoying...i'm just really desparate.

#### JohnM

##### TS Contributor
The one with the variances (grading) looks correct.

#### benchiefjr

##### New Member
benchiefjr said:
A small-engine repair shop has found that repair times have a standard deviation of 28 minutes. A new repair system is being tested, and a sample of 16 repair times produces a standard deviation of 17.3 minutes. At the 0.01 level of significance, test the claim that the new system produces a lower standard deviation than the old system.

H0 : o >= 28
H1 : o < 28

A study of smoking habits is conducted in a certain country. In a sample of 150 rural and suburban residents, 44% smoke. In a sample of 400 city residents, 52% smoke. At the 0.03 level of significance, test the claim that city residents comprise a larger proportion of smokers than rural and suburban residents.

Are these the same? If anyone could do just ONE of these, that'd be much appreciated. I still don't get this...
any idea on these other two? Thank you so much for the help thus far...

#### Lark

##### New Member
Benchiefjr,

I have always been taught that to compare standard deviations you use the F test. Sorry I don't have time to do the problem for you right now....losing too much sleep. In the back of every stat book you will find a F table. You just divide the 2 std dev values and compare to value in table (I believe the larger std is divided by the smaller), using sample size of each sample. In one of your problems it did not give sample size for one of the std dev, just assume infinite.

Lark

#### ssd

##### New Member
JohnM said:
There's no way that's the population - if so, there would be no point in running a statistical test. Count the sample size - if it's less than 30 then it's:

Hypothesis Test for m (s unknown)--One-sided t-Test

if it's >= 30 then:

Hypothesis Test for m (s unknown)--One-sided Z-Test

s is unknown because you needed to estimate it from the data.
On the first problem:

Very true : It cannot be a population by concept.... one can take any number of observations as he like.
It is a two univariate normal (assumed) distbn problem. "s unknown" - after this one is assuming that the two distributions have same s.d. Then a one sided t test is to be done.
If the two distributions do not have same s.d. then it becomes "Fisher-Behrens" problem.... which is to be solved by one of "Fiducial Approach" or " Neyman's" and "Scheffe's" approach. Another is "Smith's (and others) " approach. Depending on the standard of study it is to be decided whether one takes the two s.d.s equal or not.

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