Statistics
posted by George on .
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?

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 onesample ztest with your data included, we have:
z = .13  .10 / √[(.10)(.90)/57] >note: .90 represents 1  .10
Finish the calculation.
Use a ztable to find the critical or cutoff value at 0.01 for a onetailed test (upper tail). The test is onetailed because the alternative hypothesis is showing a specific direction (greater than).
If the ztest statistic calculated above exceeds the critical value from the ztable, reject the null. If the ztest statistic does not exceed the critical value from the ztable, do not reject the null.
I hope this will help get you started.