Question

Your company sells a tap water filter. The filter sits on a one-gallon carafe. The customer runs tap water (or water from any source) into the top of the filter mechanism. Filtered water then drains into the carafe. You hire an independent testing company to compare the efficiency of your filter versus the EPA standards. One key measurement is percent of heavy metals that remain after filtering.

The testing company draws an SRS of size n = 165 of your filters out of a large batch recently manufactured and runs highly contaminated water through each filter. The level and mix of contaminants is the same for each filter that is tested. Let X be the number of filters that meet the EPA standards (i.e., that have lower heavy metal contamination than the EPA standard).

Let p = proportion of all of your company’s filters in the current batch that fail to meet the standard. The null hypothesis is that H₀: p = 0.07 versus H_A: p ≠ 0.07. This value for p₀ was the percent of your filters that failed the test the last time that the filters were tested (i.e., 7% failed to meet the standard).

X = number of filters in the sample that failed to meet the standard. Suppose that X = 15. What is the P-value for this hypothesis test?

Group of answer choices

0.070

0.292

0.146

0.854

0.930

Answer 1

null Hypothesis:              Ho:   p=		0.070
alternate Hypothesis:    Ha: p ≠		0.070

sample success x   =		15
sample size          n    =		165
std error σp =√(p*(1-p)/n) =		0.0199
sample prop p̂ = x/n=15/165=		0.0909
z =(p̂-p)/σp=(0.091-0.07)/0.091=		1.0527
p value                          =		0.292	(from excel:2*normsdist(-1.0527)