Question

The manufacturer of Popping Joe microwave popcorn claims that no more than 2% of its kernels fail to pop. A competitor, believing that the actual percentage is much larger, tests 2,000 kernels and finds that 51 failed to pop. Can popping Joe's claim be rejected? Used a 5% level of significance and the rejection region approach

Answer 1

Let p denotes the true proportion of  kernels fail to pop.

To test against

Here

sample proportion

and sample size n = 2000

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance

Now,

The value of the test statistic

and critical value

Since , so we reject H₀ at 5% level of significance and we can conclude that there is sufficient evidence to reject Joe's claim.