To study p, the proportion of parts on hand that have type A seals, a random sam

Question

To study p, the proportion of parts on hand that have type A seals, a random sample of n=50 parts on hand are selected and 31 of them have type A seals.

(a) Give the value of an unbiased estimate of p.

(b) Is n large enough to use the large sample confidence interval for p? Whatever your answer, compute the large sample 98% confidence interval for p.

(c) Using the preliminary estimate given here, how large must n be so that and p do not differ by more than .03 units with 99% confidence.

(d) If one did not have a preliminary estimate of p, how large must n be so that and p do not differ by more than .03 units with 99% confidence.

(e) State the hypotheses used to test if more than half of the parts on hand have type A seals. With = 0.05, what is the conclusion for this test? State your conclusion in the terminology of this example; not just reject some hypothesis or do not reject a hypothesis. (f) What is the p-value for the test in part (e)?

Explanation / Answer

a) p = 31 / 50 = 0.62

b) alpha / 2 = 0.02 / 2 / 0.01 Z= 2.32

0.62 +/- 2.32 * SRQT ( 0.62 *0.38 / 50 )

0.62 +/- 0.1593

0.4607 < P < 0.7793

c)

n = Z^2 * p*q / error2

alpha / 2 = 0.005 Z =2.57

n = 2.57^2 * 0.62 * 0.38 / 0.03^2 = 1729.016 = 1730

d)

n = 2.57^2 * 0.5 * 0.5 / 0.03^2 = 1834.69= 1835

for the last question please post it in a new question

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