Question

If the null hypothesis is that the population mean is equal to 150 and a sample mean of 113 gave significant support against the null hypothesis, which of the following sample means would be certain to give support against the null hypothesis. a) 114 b) 122 c) 264 d) 112 If the p-value is less than the significance level, you would . a) reject the null hypothesis b) accept the null hypothesis c) accept the rejection region d) accept the test statistic If the null hypothesis has been accepted and there truly exists a significant difference, what type of error has been made? a) none b) type II c) type I d) type III If a directional hypothesis is legitimate, which will have greater statistical power? a) a one-tailed test b) a two-tailed test c) both will have the same power d) you can't run a two-tailed test

          If the null hypothesis is that the population mean is equal to 150 and a sample mean of 113 gave significant support against the null hypothesis, which of the following sample means would be certain to give support against the null hypothesis.
a) 114
b) 122
c) 264
d) 112

If the p-value is less than the significance level, you would .
a) reject the null hypothesis
b) accept the null hypothesis
c) accept the rejection region
d) accept the test statistic

If the null hypothesis has been accepted and there truly exists a significant difference, what type of error has been made?
a) none
b) type II
c) type I
d) type III

If a directional hypothesis is legitimate, which will have greater statistical power?
a) a one-tailed test
b) a two-tailed test
c) both will have the same power
d) you can't run a two-tailed test

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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

08/13/2022

Step 1

The null hypothesis states that the population mean is 150. A sample mean of 113 provided significant evidence against this null hypothesis. This implies that the sample mean of 113 was sufficiently far from 150 to reject the null hypothesis at a given Show more…

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If the null hypothesis is that the population mean is equal to 150 and a sample mean of 113 gave significant support against the null hypothesis, which of the following sample means would be certain to give support against the null hypothesis. a) 114 b) 122 c) 264 d) 112 If the p-value is less than the significance level, you would . a) reject the null hypothesis b) accept the null hypothesis c) accept the rejection region d) accept the test statistic If the null hypothesis has been accepted and there truly exists a significant difference, what type of error has been made? a) none b) type II c) type I d) type III If a directional hypothesis is legitimate, which will have greater statistical power? a) a one-tailed test b) a two-tailed test c) both will have the same power d) you can't run a two-tailed test

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Transcript

00:01 So we usually reject the new hypothesis if the sample mean is far away from the population mean.

00:08 Could be like a greater or smaller, but should be four.

00:12 So in our case, we are testing if our population mean is equal to 150.

00:20 And from a sample, we got that the sample mean was equals to 113.

00:25 And this sample mean gave enough evidence to reject the new hypothesis.

00:33 So, since 113 is smaller than 150, we have data value smaller than 113, smaller than 113, should also give support against the new hypothesis, because we should always go to the same direction.

00:58 If i know that a smaller number here from 150 gave enough evidence to reject the new hypothesis, i should stay in the same direction, getting smaller and smaller sample means to also reject the new hypothesis.

01:14 So from the options we have, the only number which is smaller than 113 is 112.

01:23 So the right answer will be letter d.

01:27 Now, for the other question, we have that if the p value is less than the level of significance, we usually use the letter alpha to express the level of significance.

01:41 What we should do? when the p level of a test is smaller than the alpha level, we should reject the no hypothesis.

01:52 Now, if the new hypothesis has been accepted, and there truly exist a significant difference, what type of error has been made.

02:08 So we are saying that we did not reject the new hypothesis, but we found out that we were wrong.

02:19 The new hypothesis is not true.

02:22 So we have two types of errors.

02:27 The first one is the type 1 error, which is when we reject.

02:36 This happens when we reject the no hypothesis, but it turns out that we are wrong.

02:44 We are wrong...

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