STA 291-013  Spring 2000    Computer assignment 6   Due April 18 
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Hand written your name and student id on the first page. 
Also type your name once you are inside R,  #Name.......ID......


Problem 1:  Page 466. Application 

Notice the sample size here is 35 and that's marginally a large
enough sample to use Z table (instead of a t table). So please still
use the t-table and the t.test function in R.  (Since in most cases, 
we do not know sigma and will be using s to replace sigma, there is no 
harm to use t.test even when sample size is large)

(a) and (b) 


Problem 2: Suppose in 1200 randomly selected households, 589 have
Kenmore appliances. The hypothesis to be tested are
Ho: p=0.5     Ha: p < 0.5

(a) Compute the P-value. 

(b) If we use a significance level of 0.03 (alpha), what is your conclusion? 

[end of assignment]
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One sample t-test: First put your data in a vector called data6 
(a possible example: > data6<-c(33.9, 52.4,48.6, 53.5, 43.8) remember quiz?)
To test (actually just to get p-value) Ho: mu=46.5 Ha: mu<46.5 (less than)
based on the data in data6, you do 

> t.test(data6, alternative="less", mu=46.5)        

The other possible alternatives are: "greater" and  "two.sided" 
In addition to the P-value this also computes a 95% t-confidence interval
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The function t.test can also do two-sample t-tests. Suppose you have two
(not paired) samples stored in vectors called  xbefore and xafter then do
> t.test(x=xbefore, y=xafter, alternative="less", mu=0, paired=F) 

If the data are actually paired, then change  paired=F to paired=T.

Therefore, t.test() can be used in 3 different cases: 1). one sample t-test
2). 2 sample paired t-test 3). 2 sample not paired t-test case. 
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One sample proportion test: Suppose your sample has 600 success in 1000
trials.  To test if the success propability is equal to 0.5
(actually just to get P-value)
Ho: p=0.5     Ha: p not= 0.5 (not equal)     
you do 

> prop.test(600, n=1000, p=0.5, alternative="two.sided")

The other possible alternatives are: "less"  and  "greater"
In addition to p-value this also computes a 95% confidence interval
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For further info on the use of t.etst( ) and prop.test( ) please see
the online help page that comes with R:  ?t.test   ?prop.test 
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If you are using a newer verson of R, then do 
> library(ctest)    # load the library ctest 
> binom.test(600, n=1000, p=0.5, alternative="two.sided")    
                                                     
Binom.test is similar to prop.test. The difference is that 
prop.test uses approximate computation, while binom.test uses exact 
computation [but prop.test can be used to test several samples].