Answer to Question #141556 in Statistics and Probability for HABTE HAILU

Question

Experience has shown that 20% of a manufactured product is of top quality. In one day’s
production of 400 articles, only 50 are of top quality. Write down the R programming code to
test whether the production of the day chosen is a representative sample at 95% confidence level.

Answer 1

Since the sample size is large? Normal approximation can be used. Thus, prop.test can be used.

$H_0:P=0.2$

$H_a:P\ne0.2$

The R code is

prop.test(50,400,0.2, alternative="two.sided", correct=TRUE) 
1-sample proportions test with continuity correction

data:  50 out of 400, null probability 0.2
X-squared = 13.598, df = 1, p-value = 0.0002265
alternative hypothesis: true p is not equal to 0.2
95 percent confidence interval:
 0.09501362 0.16239279
sample estimates:
    p 
0.125 

The P-value from the output is 0.0002265 which is less than 0.05 we reject the null hypothesis and conclude that the sample is not representative.