2. ACE appliance manufacturing company claims that the...

2. ACE appliance manufacturing company claims that the proportion of defectives in their brand is lower than that of PREMIER's, their next door competitor. The manager of ACE wants to demonstrate the validity of this claim. For this purpose, he selects a random sample of 36 appliances from each company and find that 3 ACE and 5 PREMIER's appliances are defective. Should we believe ACE's claim based on this data? (a) (2 points) Let ACE be population 1 and PREMIER be population 2. State the null hypothesis and alternative hypothesis (b) (4 points) Find the test statistic (c) (2 points) If the type-I error ? = 0.05, find the critical value(s) and shade the rejection region(s) (d) (2 points) Base on the type-I error ? and rejection region(s), given above, what is your conclusion?

Transcript

00:01 Okay, what we want to do is walk through a process on being able to determine to do a hypothesis test on proportion.

00:15 And so there is an appliance manufacturing company called ace, and they claim that the proportion, which we're going to let be p1 of defectives and their brand is lower than premieres, competitors.

01:11 So basically, and we're going to let that be p2.

01:15 So they're actually saying that their manufacturing company of appliances, the number of defectors, is in their brand is actually lower than their competitors.

01:28 And so this guy, he selects 36 random sample from each company.

01:44 And he kind of runs a test on them.

01:48 And he found out that three from his company were defective.

01:54 And five from premieres were defective.

02:01 Okay.

02:03 And he wants to run a test, and we're going to run a test to see if his claim is actually true or false.

02:13 And so the null hypothesis for our test, hypothesis test, is that the two proportions of defectives are exactly equal to each other.

02:26 Or another way to say that is that there is no difference between the two defective proportions.

02:36 And the alternative is the manufacturer's claim of ace, that the proportion of defectives from ace is actually lower than the proportion from premiers.

02:55 Okay.

02:56 And so there is our non -alternative hypothesis.

03:01 So the first thing we need to know, we know that it's going to be a we're calculating some z statistic.

03:08 And that is given by the sample, the difference of the two sample proportions minus zero is divided by.

03:20 And then we actually have the standard error.

03:23 So it's going to be the sample proportion 1 times 1 minus the sample proportion 1 over the sample size, which is 36.

03:35 And then we're going to add to that the second sample proportion times 1 minus the second sample proportion and divide by that sample size, which is also 36.

03:47 So the sample proportion from ace is.

03:53 3 out of 36 which is about 0 .083 and the sample proportion from premier was 5 out of 36 which is 0 .183 which just looking at the two sample proportions you would think that there is a difference in the defectives okay so we're going to put these in here we have 0 .083 minus 0 .183 minus 0 .183 and then minus 0.

04:27 And then this is divided by this long square root...

Question

Please give Ace some feedback