To test whether there is significant difference between sample proportion and population proportion using R language

 

Aim: To test whether there is significant difference between sample proportion and population

proportion.

Problem:

Suppose that 12% of apples harvested in an orchard last year was rotten. 30 out of 214 apples in a

harvest sample this year turns out to be rotten. At .05 significance level, can we reject the null

hypothesis that the proportion of rotten apples in harvest stays below 12% this year?

R – Code:-

The null hypothesis is that p ≤ 0.12. We begin with computing the test statistic.

>pbar=30/214

# sample proportion

> p0=0.12

# hypothesized value

> n=214

# sample size

> z=abs((pbar-p0)/sqrt(p0*(1-p0)/n))

>z

# test statistic

[1] 0.908751

We then compute the critical value at .05 significance level.

>alpha=0.05

>z.alpha=qnorm(1-alpha/2)

>z.alpha# critical value

[1] 1.959964