Hypothesis Testing Question

Peyton Manning

Hey guys,

Im currently revising for a Statistics exam on Monday, and have been doing a few past papers. The only topic im really having trouble with is hypothesis testing for samples as I missed the topic in lectures. Theres a particular type of question that comes up every year that follows th sam structure so once I figure out one of them, hopefully I should get the rest. Here goes:

Basically, youre given a frequency distribution for amounts spent in a store as follows:

Amount Spent (£)..............Frequency
0-20....................................60
20-40..................................100
40-60..................................125
60-80..................................75
80-100.................................40

In part (a), Ive calculated the Arithmetic Mean as 46.75 and the Standard Deviation as 23.79 and the first decile as 13.33.

In part (b), Ive calculated the 95% confidence interval for the population mean as (49.08142) and/or (44.41858).

Part (c) is where I get stuck. Im given another store and am to test the hypothesis that there is no significant difference between the average amounts spent in the 2 stores. The figures given for this new store are:

n = 300
Sd = 21
Mean = 49

Where the feck do I begin!?

MathsManiac

Try this:

http://stattrek.com/AP-Statistics-4/Unpaired-Means.aspx

Peyton Manning

MathsManiac wrote: »

Try this:

http://stattrek.com/AP-Statistics-4/Unpaired-Means.aspx

Tried it, still struggling

Im afraid ill probably need a walk through on this, really need to get my head round it :(

Grudaire

Archimedes wrote: »

Tried it, still struggling

Im afraid ill probably need a walk through on this, really need to get my head round it :(

Look up hypothesis testing on this page, it's pretty walkthrough:

http://www.computing.dcu.ie/~wuhai/CA151.htm

MathsManiac

Ok. See if this is enough:

You've to do a t-test.

The wikipedia article is pretty good:
http://en.wikipedia.org/wiki/Student's_t-test
...and in particular, see 4.2.3, dealing with the relvant test statistic for unequal sample sizes and unequal variances.

In your case, you have X1 and S1 from part (a) of the question, and n1=400.
X2, S2 and n2 are given as 49, 21 and 300 respectively.

Plug these values into the equations in section 4.2.3 of the wikipedia article, to get your test-value for t, and the number of degrees of freedom. Look this up in your t-distibution tables to see if it lies beyond the relevant critical value.

Grudaire

The formula is (x1 - x2) / sqrt( (Var1)/n1 + (Var2)/n2)

And you compare this to the Z tables (as n is large)

MathsManiac

Cliste is correct in that, since n is large, the t-distribution is so close to the z-distribution that the z-test described is sufficiently accurate. Even if you do the more exact t-statistic calculation, the number of degrees of freedom in this example is so large that in an exam you'll have to use z-tables anyway, since the t-tables probably won't go up that far. (Outside an exam context, you could use an online calculator for the t-statistic.)

If you're confident that the exam question you're likely to get will similarly involve large sample sizes, then you can safely ignore the t-statistic version and stick with Cliste's suggestion.

Peyton Manning

Cliste wrote: »

The formula is (x1 - x2) / sqrt( (Var1)/n1 + (Var2)/n2)

And you compare this to the Z tables (as n is large)

Silly question, but Var1 and Var2 are calculcated how exactly? Sorry, my head is just fried lately

I appreciate all the help...

Grudaire

The varience? Good luck in the exam you'll need it:D

Firstly all these formulae are in the log tables (I assume you'll get the statistics ones)

Secondly add all the (x - E(x))/n-1

(Standard deviation squared if that helps)