Question

Assume that X = 40 defects out of a sample size of n = 400. You wish to determine whether the sample supports the hypothesis that the fraction of defects in the population is 12%. 1. What is the sample proportion of defective items? (2 Decimal Places) 2. Construct the appropriate hypothesis test. Identify HO and H1. 3. What is the standard error of the proportion? (3 Decimal Places) 4. What is the appropriate test statistic? (4 Decimal Places) 5. For a -0.10, what is the appropriate critical value? (4 Decimal Places) 6. From what distribution (z ort)? Ift, with how many degrees of freedom? 7. At a 90% level of confidence, what is your statistical decision? HTML Editor BI V AA- IE 11 *, SE - O N V M O D T TT 12pt - Paragraph -

Answer 1

Solution' Given that na 400 x=40 x=0.10 P = 40 = 0.10 400 Po= 12 % = 0.12 Ho:p= 0.12 Hiip to.12 This is two-tailed test 4) Test statistic, I z= o-po Poliepos v n Z 0-10 - 0.12 0.1211-0./2) 400 z=1.2310 The test statistic = 1-2310

- X-oilo - Zx= 20.10 - +/- 1.6400 Zc = -1.6400 and 2c = 1.6400 5) The critical value - +/- 1.6400 6) The 2-distribution, 1.2310 < t-1.6400 Test statistic critical value. - Reject Ho. Reject the hall hypothesis. p-Value = 0.2184 0.2184 > 0.10 P-value > x fail to reject Ho conclusion! There is not enough evidence to claim that the pis different than po, at a=0. lo significance level.