Uw madison will add dairy vending machines milk cheese curds...

Name: uw madison will add dairy vending machines milk cheese curds ice cream etc to a few classroom buildings if the student body president is convinced that more than 20 percent of the students w 95418
Uploaded: 2022-05-05T16:01:15-08:00
Duration: 8 min 22 s
Channel: Shaiju T
Description: uw madison will add dairy vending machines milk cheese curds ice cream etc to a few classroom buildings if the student body president is convinced that more than 20 percent of the students w 95418

UW Madison will add dairy vending machines (milk, cheese curds, ice-cream, etc.) to a few classroom buildings if the student body president is convinced that more than 20 percent of the students will use them. A random sample of n students will be selected and asked whether or not they would use the vending machines. A large-sample test for proportions at the significance level of .05 will be performed. The null hypothesis that the proportion of all students who would use the vending machines is at most 20 percent will be tested against the alternative that more than 20 percent of all students would use them. For which of the following situations would the power of the test be highest? (Do not try to compute power for each of these...just use what you know about what factors influence power)

Transcript

00:01 Hello everyone we are going to solve a question in this question we are given.

00:04 N is equals to 100 and in a part that is first part of the question we have to write the hypothesis.

00:12 We have to write hypothesis.

00:14 So we have null hypothesis which is denoted by h0.

00:18 This stated as that p is equals to 1 divided by 3 and alternative hypothesis that is denoted by h1 is stated as p is greater than 1 divided by 3.

00:30 3 and in second part of this question we have to tell that for what value of proportion we reject null hypothesis so here we let consider we consider alpha is equal to 0 .05 and for this we find value of z so this is equal to p cap minus p and this divided by square root of p multiplied with 1 minus p divided by n now putting the values here we have this z is equals to p cap minus 0 .33333 and divided by square root of 0 .333 and this multiplied with 1 minus 0 .33333 and this divided by 100 and on solving this we have z is equals to p cap minus 0 .3 333 3 and this 333 and this divided by 0 .0471.

01:36 Now we reject null hypothesis.

01:40 We reject we reject null hypothesis h0 if p value, p value is less than alpha and alpha we take are taken as 0 .05.

01:54 So we're going to find the p value and for p value this is probability.

01:58 Z is greater than p cap minus 0 .3.

02:02 333 and this divided by 0 .0471 is less than 0 .05 so from here we have that this this peak up from the table we have that this p cap minus 0 .3333 divided by 0 .0471 is greater than 1 .64 and from here we have that p cap minus 0 .3 333 3 divided by 0 .0471 is greater than 1 .64 and from here we have that p cap is equals to 0 .333 plus 0 .0471 multiplied with 1 .64.

02:40 And on solving we have this peak up, sorry, here we have peak up greater than, as there is a greater sign.

02:48 So there we have peak up greater than 0 .4105.

02:52 So from here we have therefore, therefore minimum value, minimum value, minimum value of sample proportion of sample proportion should be 0 .4105 for which we reject null hypothesis h0.

03:27 Moving towards the third part of the question.

03:29 In third part it is given that at 5 % level of significance level of significance p cap we found is equal to approximately 0 .42 and we have to find power.

03:49 So the formula for power is equal to probability that z is greater than test statistic that is p cap minus p and is divided by a square root of p multiplied with 1 minus p...

Question

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