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 overfilled, then they stop production to fix the machine. they define overfilled to be more than 1 ounce above the weight on the package. the engineer weighs 100 bags and finds that 21 of them are overfilled. 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? a. z = - 1.68 b. z = 4 c. z = - 1.47 d. z = 1.68

Explanation:

Step1: Calculate sample proportion

The sample size $n = 100$ and the number of over - filled bags $x = 21$. The sample proportion $\hat{p}=\frac{x}{n}=\frac{21}{100}=0.21$.

Step2: Identify hypothesized proportion

The hypothesized proportion $p_0 = 0.15$.

Step3: Calculate the test statistic formula

The test statistic for a one - sample proportion test is $z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$.

Step4: Substitute values into the formula

Substitute $\hat{p}=0.21$, $p_0 = 0.15$ and $n = 100$ into the formula:

$$
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Answer:

D. $Z = 1.68$