A large automobile insurance company selected samples of...

Name: a large automobile insurance company selected samples of single and married male pol icy holders and recorded the number who made an insurance claim over the preceding three year period single policy
Uploaded: 2019-07-21T22:46:03-08:00
Duration: 6 min 40 s
Channel: Srikar Katta
Description: a large automobile insurance company selected samples of single and married male pol icy holders and recorded the number who made an insurance claim over the preceding three year period single policy

A large automobile insurance company selected samples of single and married male pol-icy holders and recorded the number who made an insurance claim over the preceding three-year period. Single Policy holders Married Policy holders n1= 400 Number making claims = 76 & n2= 900 Number making claims = 90. a) Compute the test statistic. b)Compute the critical value at a?= 0.05 level of significance. c) What is your conclusion based on the critical value? d) Compute the 95% confidence interval estimate of the difference between the population proportions. Can you conclude that the two proportions are significantly different?

Transcript

00:01 In this problem, we're trying to see whether the claims rates differ between single and male policyholders.

00:06 So our null hypothesis is going to be that they are equal.

00:12 So the population proportion for our first sample is equal to the population proportion for our second sample.

00:17 And our alternative hypothesis is going to be that these are not equal.

00:23 And we can also write this as a difference of proportions as so.

00:31 And now with this we have to come up with a test statistic because we're working with population proportions.

00:38 We're going to find a z score and the formula for a z score is equal to the population proportions, the difference between the sample proportions, sorry, divided by the square root of the pooled variance times one minus the pooled variance times times one over the first sample size plus one over the second sample size.

01:09 So let's find out all this information.

01:11 The first thing we need to find is this difference or these sample proportions.

01:19 So the sample proportion for the first sample is equal to 76 divided by 400, which is approximately 0 .19.

01:32 And for the second sample, it is 90 over 900, which is equal to 0 .1.

01:42 So with these, we have to come up with a pooled variance for this part right here.

01:50 Now, pooled variance is going to be equal to 0 .19, or is going to be equal to the frequency in each population divided by the sample sizes of each population.

02:07 So we get a pooled variance of approximately 0 .128.

02:15 Now with this we can come up with this z test statistic.

02:20 So this is equal to the difference of sample proportions, so that is 0 .19 minus 0 .1 .1 divided by square root of 0 .128, our pooled variance times 1 minus 0 .128 times 1 .128 times times 1 over 400 plus 1 over 900.

02:42 And after all of this, we get a z test statistic of approximately 4 .49.

02:48 So what does the seed test statistic represent? if we draw a normal curve, the z test statistic, is equal 0 here, represents where it is 4 .49 standard deviations away from z equals 0.

03:04 And because we're looking at a difference, we are seeing that we are using a two -sided z test, so we not only need the area to the right of z equals 4 .49, we also need the area to the left of z equals negative 4 .49 because it is two -sided...

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