Use Excel, software, a website, or a table to find the...

Use Excel, software, a website, or a table to find the $p$-value for each of the standardized scores, taking into account whether the test is one-sided or two-sided. (Round your answers to five decimal places.) (a) $z = 2.18$, two-sided test (using $z$, not $t$) 0.98537 (b) $z = 2.00$, one-sided test 0.97725 (c) $z = 4.08$, one-sided test 0.000038

Transcript

00:01 All right.

00:01 So in the given question, we have four parts and we have different four different hypothesis test and we need to determine the p value for each.

00:10 So for the first one, the null hypothesis is that population proportion is less than equal to 0 .65 and alternative hypothesis is that population proportion is greater than 0 .65, right? now here the size of the sample is 84 and the number of favorable outcomes is 63.

00:29 So here the sample.

00:31 Proportion this will be equal to x divided by n that is 63 upon 84 right so this will be equal to 0 .75 right now the formula to compute the test statistic value this is equal to sample proportion minus population proportion divided by a square root of the population proportion into one minus population proportion upon the sample size right so this is the formula that we will be using in all the all other parts as well right so here our test statistic value will be equal to 0 .75 minus 0 .65 divided by a square root of 0 .65 into 1 minus 0 .65 divided by 84 right so this is equal to 1 .92 all right so the p value for this will be equal to the probability of z greater than 1 .92 and this we can obtain from the z table it is 0 .073 right moving on to the next part of the question here our null hypothesis is that the population proportion is 0 .30 while the alternative hypothesis is that population proportion is different from 0 .30 so this one is a two -tailed hypothesis test right now in this case the size of the sample is 35 while the number of favorable outcomes is 16 so for this one the sample proportion is equal to 0 .457 all right now we again we'll use the same formula so this is 0 .457 minus 0 .30 divided by square root of 0 .30 into 1 minus 0 .30 divided by 0 .30 divided by 35 right so the test statistic value here is this is 0, sorry 2 .0 so the p value for this one this will be equal to twice the probability of z greater than 2 .03, right? so the p value obtained in this case is 0 .0424.

02:53 All right? in the last part of the question, it says our null hypothesis is that the population proportion is greater than 0 .10 while the alternative hypothesis is that population proportion is less than 0 .10.

03:08 Then 0 .10.

03:10 So this is a left -tailed hypothesis test.

03:14 Here we have a sample who size is 116 with number of favorable outcomes as 4.

03:20 Right...

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