54 consider the following hypotheses ho p 038 ha p 038...

54. Consider the following hypotheses: H0: p > 0.38 HA: P < 0.38 Calculate the p-value based on the following sample information: a. x = 22; n = 74 b. x = 110; n = 300 c. p = 0.34; n = 50 d. p = 0.34; n = 400 55. Which sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?

Transcript

00:01 Right, given question, we have been provided a hypothesis.

00:04 So here the null hypothesis says that the population average is greater than equal to 0 .38 versus the alternative hypothesis that it is less than 3 .38.

00:13 Right now we have been asked to compute the p value on the basis of the given information.

00:18 So for the first part, it says that here x is equal to 22 and is equal to 74.

00:27 Right.

00:27 Now here the first okay so here first we obtain the sample proportion right so the sample proportion for first it is 22 divided by 74 that is 0 .2973 right so we first need the test statistic value so this is equal to sample proportion minus population proportion upon square root of population proportion into one minus population proportion divided by and now here the population proportion remains the same right for all the parts and we just need to change the value of the sample proportion according to the information provided right so the same formula this one we will be using for the all four parts right so this is equal to 0 .2973 minus 0 .38 divided by square root of 0 .38 into 1 minus 0 .38 divided by n here is 74 so this is equal to minus 1 .4657 now here this is a left tail test so the the p value it is equal to the probability of z less than minus 1 .4657 right so this will be equal to 0 .0714 right moving on to the next part here n is equal to 300 x is equal to 100 n so the sample proportion here will be 110 divided by 300 this is equal to 0 .367 right so z will be equal to here 0 .3667 minus 0 .38 divided by square root of 0 .38 into 1 minus 0 .38 divided by 300, right? so this is equal to minus 0 .4746.

02:17 Right.

02:18 Now, here, the p value will be equal to the probability of z less than minus 0 .4746.

02:26 And this is equal to 0 .31746.

02:27 And this is equal to 0 .317...

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