# Hypothesis Testing

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#### thedeath

##### New Member
Need to know the test that will be performed on the following question:

The data comprises hours devoted to patient care per week for practitioners in conventional and alternative medical practices.

Question:
Can we infer that the mean amount of time devoted to patient care per week by doctors using conventional methods exceeds that of doctors using alternative methods? Test at the 10% level of significance.

What test will be performed:
Hypothesis Test for m (s known)--Two-sided Z-Test
Hypothesis Test for m (s known)--One-sided Z-Test
Hypothesis Test for m (s unknown)--Two-sided t-Test
Hypothesis Test for m (s unknown)--One-sided t-Test
Hypothesis Test for p--One-sided Z-Test

#### JohnM

##### TS Contributor
In the problem are you given s (std dev) and n (sample size)? Can't answer your question unless I know this.

#### thedeath

##### New Member
Here is all the data that is given:

Alternative
(hours per week)

54
60
49
45
53
44
48
49
51
54
51
53
53
51
54
39
52
48
51
52
52
51
25
52
47
45

Conventional
(hours per week)

50
52
52
53
52
58
53
58
51
50
55
54
52
57
54
57
56
53
50
49
52
47
49
48
53
84​

In previous parts of the question it was asked to calculate the SD, mean, variance of the above data using excel, and all that information is already with me.
And this itself is the population and not the sample.

#### JohnM

##### TS Contributor
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.

#### thedeath

##### New Member
The question does not specify if its population or a sample only that:

"The data comprises hours devoted to patient care per week for practitioners in conventional and alternative medical practices."

And each table includes 26 units of data.

When you say: Count the sample size - if it's less than 30 then it's: are you referring to the total no. or the data in an individual table.

#### JohnM

##### TS Contributor
I think it's safe to assume that it's a sample - if it were the entire population, then it would be pointless to do a statistical test (the purpose of a statistical test is to use sample data to draw an inference about the population - if you have the entire population, there's no inference to draw - you have all the info you need.)

Count n in an individual table. Since it's n=26 compared to n=26, use a t-test.

#### thedeath

##### New Member
Here is the result obtained (the attachment contains the .xls file):

Alternative, Conventional
Mean 49.34615385 53.80769231
Variance 41.43538462 46.80153846
Observations 26 26
Hypothesized Mean Difference 0
df 50
t Stat -2.421843846
P(T<=t) one-tail 0.009555236
t Critical one-tail 1.298712959
P(T<=t) two-tail 0.019110472
t Critical two-tail 1.675905423

What will be the conclusion. The question stated: Can we infer that the mean amount of time devoted to patient care per week by doctors using conventional methods exceeds that of doctors using alternative methods?

#### JohnM

##### TS Contributor
OK, well - what do you think? Sometimes it's better if we let students answer their own questions...

#### thedeath

##### New Member
Well have not been through the theoretical concepts as yet. Have had to do this on excel so will take time till i can determine the conclusion.

#### Lark

##### New Member
Hope yous don't mind if I but in.

The difference between population and sample is rather interesting...

I guess if you are not interested in future groups (note, I did not say sample here) then you could consider many samples as populations. But it makes sense what John is saying: if you consider the groups "populations' then you have all the information about your groups. For example: the entire "population" of the earth, say you compare the heights of men and women; if you consider this a population then you can't talk about whether the difference in mean is stat diff but if you consider that the population of the earth is increasing then you could consider the current population as a sample and then you could talk about whether there is a stat difference.

John, am I on tera firma here?

Lark

#### BioStatMatt

##### TS Contributor
It is also interesting to note: if the population is normally distributed, and the sd is known, then a z-test is appropriate regardless of the sample size. This is true because, the sample mean xbar will be exactly N(mu, (sigma^2)/n).

~Matt

#### JohnM

##### TS Contributor
Yep. But I've never seen a situation where the population standard deviation is known.....

#### benchiefjr

##### New Member
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!

#### benchiefjr

##### New Member
would they ALL be done like that?

EDIT : Is there a way I could contact you on AIM or MSN in case i need future help?

#### benchiefjr

##### New Member
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.

#### JohnM

##### TS Contributor
For testing variances, you would use a chi-squared distribution.

#### benchiefjr

##### New Member
the example shows tables...there's no tables here.

#### benchiefjr

##### New Member
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...

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