Historically, a manufacturer finds that 1% of integrated circuits of a certain type fail during burn-in testing. Burn-in testing results (pass/fail) on the latest shipment of 10,500 circuits are to be analyzed using hypothesis testing to compare the failure rate of the this shipment with the historical norm. Of these circuits, 125fail. Is this good evidence that the failure rate differs from the historical rate? To decide, conduct an hypothesis test at the 0.01significance level.

(1) The observed value of the (unstandardized) test statistic is

(2) To four decimal places, the p-value for the continuity-corrected large sample test is

(3) Does the test reject the null hypothesis at the 0.01 level?

AND

Various studies have shown that approximately 10% of individuals in developed countries are left handed, but that there is a 2% difference between the genders, with the percentage of males who are left handers being about 2% higher than the corresponding percentage of females. A study is conducted to see if this pattern holds in other parts of the world. A random sample of 150 male and 200 female Amazon natives is obtained and the proportions of left handers in each gender compared. If 16 of the males and 21 of the females are left handed, conduct an hypothesis test on whether or not for the Amazon native population equals the value for the developed world. Specifically, answer the following:

(1) To four decimal places, the observed value of the standardized test statistic is

(2) To four decimal places, the p-value is

(3) Does the test reject the null hypothesis at the 0.01 level?