Two different types of injection-molding machines are used to form plastic parts. a part is considered defective if it has excessive shrinkage or is discolored. two random samples, each of size 300, are selected, and 15 defective parts are found in the sample from machine 1, and 8 defective parts are found in the sample from machine 2.
(a) is it reasonable to conclude that both machines produce the same fraction of defective parts, using ? = 0.05? find the p-value for this test.
(b) construct a 95% confidence interval on the difference in the two fractions defective.
(c) suppose that p1 = 0.05 and p2 = 0.01. with the sample sizes given here, what is the power of the test for this two-sided alternative?
(d) suppose that p1 = 0.05 and p2 = 0.01. determine the sample size needed to detect this difference with a probability of at least 0.9.

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step-by-step explanation:

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.

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for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for