SOLUTION: A supplier of USB flash claims that more than 11% of the USBs are defective. In a random sample of 167 USBs, it is found that 37 are defective, but the supplier claims that this is

Question 1200911: A supplier of USB flash claims that more than 11% of the USBs are defective. In a random sample of 167 USBs, it is found that 37 are defective, but the supplier claims that this is only a sample fluctuation. At the 0.05 level of significance, test the supplier's claim that more than 11% are defective.
a. Is this (a: one sample mean test, b: two sample mean test, c: one proprtion test, d: ch-square test)
b. Since the test statistic (round to 2 decimals):
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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 https://www.statskingdom.com/111proportion_normal1.html

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.

RELATED QUESTIONS
----------- A simple random sample of 300 is selected from a large shipment and testing... (answered by robertb)

A simple random sample of 300 is selected from a large shipment and testing reveals that... (answered by Boreal)

Five percent of computer parts produced by a certain supplier are defective. What is... (answered by KawaiiKittenGal<3)

Ten percent of computer parts produced by a certain supplier are defective. What is the... (answered by stanbon)

Suppose that an automobile parts wholesaler claims that .5 percent of the car batteries... (answered by ewatrrr)

A store sells three types of flash drives: brand A, brand B, and brand C. Of the flash... (answered by ikleyn)

5. Five percent of computer parts produced by a certain supplier are defective. What is... (answered by richard1234)

A manufacturer claims that fewer than 6% of its fax machines are defective. In a random... (answered by stanbon)