Conduct the following test at the ? = 0.05 level of...

Conduct the following test at the ? = 0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the critical value. Assume that the samples were obtained independently using simple random sampling. Test whether p1 ? p2. Sample data are x1 = 28, n1 = 255, x2 = 38 and n2 = 302. (a) Determine the null and alternative hypotheses. Choose the correct answer below. H0: p1 = p2 versus H1: p1 < p2 H0: p1 = p2 versus H1: p1 > p2 H0: p1 = p2 versus H1: p1 ? p2 (b) The test statistic z0 is -0.58. (Round to two decimal places as needed.) (c) The critical values are ± . (Round to three decimal places as needed.) Test the null hypothesis. Choose the correct conclusion below. Do not reject the null hypothesis. Reject the null hypothesis.

Transcript

00:01 Alright, so in the given question, we have been asked to conduct a hypothesis test.

00:06 So here, the null hypothesis is that the two population proportions are equal, and the alternative hypothesis will be that the two population proportions are different, right? so this will be a two -tailed hypothesis test.

00:24 All right.

00:25 Now, here we have the following information, that is, size of the first sample is 30.

00:31 Sorry, this is all right.

00:36 Okay.

00:37 Size of the first sample is 254 with the number of favorable outcomes as 30.

00:42 And the size of the second sample is 302 with the number of favorable outcomes as 36.

00:48 So we have to first compute the sample proportions before we can proceed to the next part, which is the calculation of test statistics, right? so the first sample proportion is x1 divided by n1, that is will be equal to.

01:03 This is 0 .1181 and second is x2 divided by n2 which is equal to 0 .1192 right now we also need the pool sample proportion which is equal to x1 plus x2 right so this is equal to 30 plus 36 upon 254 plus 302 so this is equal to 0 .1187 now we can move on to the next part that is the calculation of test statistics so the formula here is sample proportion difference between the two sample proportion divided by square root of pool proportion into one minus the pool proportion into one upon n1 plus one upon n2 right so this will be 0 .1181 minus point one 192 divided by square root of this is point 1187 into 0 .8 .8 .7 into 0 .8 .8 .0 .8 .0 .8 .0 .5 .5.

02:04 81813 into 1 upon 254 plus 1 upon 300 so when we solve this it is equal to minus 0 .04 so that's the value for test statistics now the third part okay so we have alpha as 0 .10 here so our critical value it corresponds to the value of z alpha by 2 because it's a two tail test so our critical values will be for 0 .05 so this will be plus minus 1 .645...

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