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SKILL BUILDER I In Exercises 6.135 to 6.140, use the $t$-distribution and the sample results to complete the test of the hypotheses. Use a 5% significance level. Assume the results come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal. 6.135 Test $H_0: \mu = 15$ vs $H_a: \mu > 15$ using the sample results $\bar{x} = 17.2$, $s = 6.4$, with $n = 40$. 6.136 Test $H_0: \mu = 100$ vs $H_a: \mu < 100$ using the sample results $\bar{x} = 91.7$, $s = 12.5$, with $n = 30$. 6.137 Test $H_0: \mu = 120$ vs $H_a: \mu < 120$ using the sample results $\bar{x} = 112.3$, $s = 18.4$, with $n = 100$. 6.138 Test $H_0: \mu = 10$ vs $H_a: \mu > 10$ using the sample results $\bar{x} = 13.2$, $s = 8.7$, with $n = 12$. 6.139 Test $H_0: \mu = 4$ vs $H_a: \mu \ne 4$ using the sample results $\bar{x} = 4.8$, $s = 2.3$, with $n = 15$. 6.140 Test $H_0: \mu = 500$ vs $H_a: \mu \ne 500$ using the sample results $\bar{x} = 432$, $s = 118$, with $n = 75$.

          SKILL BUILDER I
In Exercises 6.135 to 6.140, use the $t$-distribution and the sample results to complete the test of the hypotheses. Use a 5% significance level. Assume the results come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal.
6.135 Test $H_0: \mu = 15$ vs $H_a: \mu > 15$ using the sample results $\bar{x} = 17.2$, $s = 6.4$, with $n = 40$.
6.136 Test $H_0: \mu = 100$ vs $H_a: \mu < 100$ using the sample results $\bar{x} = 91.7$, $s = 12.5$, with $n = 30$.
6.137 Test $H_0: \mu = 120$ vs $H_a: \mu < 120$ using the sample results $\bar{x} = 112.3$, $s = 18.4$, with $n = 100$.
6.138 Test $H_0: \mu = 10$ vs $H_a: \mu > 10$ using the sample results $\bar{x} = 13.2$, $s = 8.7$, with $n = 12$.
6.139 Test $H_0: \mu = 4$ vs $H_a: \mu \ne 4$ using the sample results $\bar{x} = 4.8$, $s = 2.3$, with $n = 15$.
6.140 Test $H_0: \mu = 500$ vs $H_a: \mu \ne 500$ using the sample results $\bar{x} = 432$, $s = 118$, with $n = 75$.

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skill builder i in exercises 6135 to 6140 use the t distribution and the sample results to complete the test of the hypotheses use a 5 significance level assume the results come from a rando 56723

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ana Carolina Da Cruz

09/15/2022

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2$, $s = 8.7$, and $n = 12$. The significance level is $\alpha = 0.05$. Show more…

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SKILL BUILDER I In Exercises 6.135 to 6.140, use the $t$-distribution and the sample results to complete the test of the hypotheses. Use a 5% significance level. Assume the results come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal. 6.135 Test $H_0: \mu = 15$ vs $H_a: \mu > 15$ using the sample results $\bar{x} = 17.2$, $s = 6.4$, with $n = 40$. 6.136 Test $H_0: \mu = 100$ vs $H_a: \mu < 100$ using the sample results $\bar{x} = 91.7$, $s = 12.5$, with $n = 30$. 6.137 Test $H_0: \mu = 120$ vs $H_a: \mu < 120$ using the sample results $\bar{x} = 112.3$, $s = 18.4$, with $n = 100$. 6.138 Test $H_0: \mu = 10$ vs $H_a: \mu > 10$ using the sample results $\bar{x} = 13.2$, $s = 8.7$, with $n = 12$. 6.139 Test $H_0: \mu = 4$ vs $H_a: \mu \ne 4$ using the sample results $\bar{x} = 4.8$, $s = 2.3$, with $n = 15$. 6.140 Test $H_0: \mu = 500$ vs $H_a: \mu \ne 500$ using the sample results $\bar{x} = 432$, $s = 118$, with $n = 75$.

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Transcript

00:01 So in letter a here, we can say that since n is at least 30, we can still perform the test.

00:11 So we can perform the test statistic.

00:17 If the sample size was smaller than this, we would suppose that the population will be normally distributed.

00:24 So since we have a sample size which is quite high, in our case 40, we can still perform the task.

00:32 But using the t student distribution.

00:35 Now in letter b, we need to compute the test statistic.

00:38 The test statistic here, like i said, is given by the t student here.

00:43 And in this case, we need to put this x bar minus the value that we are testing in our hypothesis, which is 45, divided by the sample standard deviation, which is 8 .5, divided by the square root of the sample size.

01:00 So this here, if you can, compute you're going to get this test statistic.

01:06 Now in letter c we need to just draw a t student with the area that represents the p value.

01:14 So the t student is symmetric.

01:17 So this t student here has degrees of freedom.

01:21 In our case the degrees of freedom is the sample size minus 1 so in our case 39.

01:27 And the p value here since the test is to tail, why to tail? because the alternative has, in this case, the different sign.

01:39 So it is like a non -directional test.

01:42 So because of this, this means that we have two areas that represents the p value.

01:48 So the p value will be the sum of these two areas.

01:51 And how can we find this? we need to put this number here.

01:55 The positive will be here and the negative will be here...

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