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 15% 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 100 bags and finds that 21 of them are over-filled.

He plans to test the hypotheses: H0: p = 0.15 versus Ha: p > 0.15 (where p is the true proportion of overfilled bags).

What is the test statistic?

Z = 1.68
Z = -1.68
Z = 4
Z = -1.47

Answer 1

Answer:

Option A) 1.68                

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 100

p = 15% = 0.15

Number of bags overfilled , x = 21

First, we design the null and the alternate hypothesis  

$H_{0}: p = 0.15\\H_A: p > 0.15$

Formula:

$\hat{p} = \dfrac{x}{n} = \dfrac{21}{100} = 0.21$

$z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Putting values, we get,

$z = \dfrac{0.21-0.15}{\sqrt{\dfrac{0.15(1-0.15)}{100}}}\\\\z = 1.68$

Thus, the correct answer is

Option A) 1.68