A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 57 microwaves that are 5 years old, 13% needed repairs. At á=0.01, can you reject the maker’s claim that no more than 10% of its microwaves need repair during the first five years of use?

Answer 1

Null hypothesis:
Ho: p < or = .10 -->meaning: population proportion is less than or equal to .10
Alternative hypothesis:
Ha: p > .10 -->meaning: population proportion is greater than .10

Using a formula for a binomial proportion one-sample z-test with your data included, we have:
z = .13 - .10 / √[(.10)(.90)/57] -->note: .90 represents 1 - .10

Finish the calculation.

Use a z-table to find the critical or cutoff value at 0.01 for a one-tailed test (upper tail). The test is one-tailed because the alternative hypothesis is showing a specific direction (greater than).

If the z-test statistic calculated above exceeds the critical value from the z-table, reject the null. If the z-test statistic does not exceed the critical value from the z-table, do not reject the null.

I hope this will help get you started.