Question

The proportion of defective items is not allowed to be over 12%. A buyer wants to test whether the proportion of defectives in his shipment of 1000 items exceeds the allowable limit. The buyer takes a SRS of 100 items and finds that 17 are defective.

State the null and alternative hypotheses for this test.

		H0: π = 0.12 versus Ha: π = 0.17
		H0: π = 0.12 versus Ha: π > 0.12
		H0: π = 0.17 versus Ha: π > 0.12
		H0: π = 0.12 versus Ha: π < 0.17

B) Compute the appropriate test statistic (CF is important here).

		z = 1.24
		z = 1.62
		z = 1.08
		z = 1.31
		z = 1.46

C) What is the p-value?

		0.0637
		0.0688
		0.0598
		0.0812
		0.0526

D) In real life terms, what is your conclusion?

		Evidence suggests that the proportion of defective units exceeds the allowable limit of 12%.
		Evidence suggests that the proportion of defective units is significantly lower than the allowable limit of 12%.
		There is insufficient evidence to suggest that the proportion of defective units exceeds the allowable limit of 12%.

Answer 1

Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

n = 1000
p^ = x/n = 17/100 = .17

Null hypothesis: Ho: p = .12,
Alternate hypothesis: Ha: p > .12

2nd option is correct

B. test statistic ,

Z = (p^-p)/sqrt(p*p'/n) = (.17-.12)/sqrt(.12*.88/100) = +1.3311
Answer is Z = 1.31

p-value = P(Z>z) = P(Z>1.31) = 0.817
Answer is 0.0812

Answer is :

3rd option is correct.

There is insufficient evidence to suggest that the proportion of defective units exceeds
the allowable limit of 12%