Question

A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 16% of bags are over-filled then they stop production to fix the machine. They define over-filled to be more than 1 ounce above the weight on the package.

The engineer weighs 111 bags and finds that 36 of them are over-filled. He plans to test the hypotheses H0: p = 0.16 versus Ha: p > 0.16. What is the test statistic?

z =

(Please round your answer to two decimal places if necessary.)

Answer 1

Solution =

The null and alternative hypothesis are,

H0: p = 0.16 ..... Null hypothesis

Ha: p > 0.16 ..... Alternative hypothesis

Here, n = 111 , x = 36

   = x/n   = 36/111 = 0.32

The test statistic is,

z =   - /

= 0.32 - 0.16/0.16(1-0.16) / 111

= 4.72

Answer :

The test statistic is z = 4.72