Question 1200911
population p = .11
population q = 1 - .11 = .89
sample size is 167.
37 are defective.
sample p = 37/167 = .2215568862
standard error of the test is equal to sqrt(population p * population q / 167) = sqrt(.11 * .89 / 167) = .0242121363.
z-score = (.2215568862 - .11) / .0242121363 = 4.607478034
area to the right of that = .000002040040862.
that's significantly less than the critical p-value of .05.
the probability  that the resuls is a fluctuation in smple means is pretty close to 0.
the conclusion i that the preponderance of the evidence indicates that more than 11% of the USBs are defective, rejecting the claim that it's no more than 11%.



this is a one sample proportion test.
the critical p-value is .05
the test p-value is 0, rounded to two decimal places.


here are the results using the proportion calculator at <a href = "https://www.statskingdom.com/111proportion_normal1.html" target = "_blank">https://www.statskingdom.com/111proportion_normal1.html</a>


<img src = "http://theo.x10hosting.com/2023/050403.jpg">


differences between the calculator numbers and the ones i calculated have an insignificant impact to the result and are more than likely due to rounding differences.