A sample of 36 observations is selected from a normal...

Name: a sample of 36 observations is selected from a normal population the sample mean is 21 and the population standard deviation is 5 conduct the following test of hypothesis using the 005 signi 04406
Uploaded: 2022-05-01T13:55:45-08:00
Duration: 3 min 19 s
Channel: Sheryl Ezze
Description: a sample of 36 observations is selected from a normal population the sample mean is 21 and the population standard deviation is 5 conduct the following test of hypothesis using the 005 signi 04406

A sample of 36 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level. $H_0: \mu \le 20$ $H_1: \mu > 20$ a. Is this a one- or two-tailed test? "One-tailed"—the alternate hypothesis is greater than direction. "Two-tailed"—the alternate hypothesis is different from direction. b. What is the decision rule? Note: Round your answer to 2 decimal places. $H_0$ when z >

Transcript

00:01 So we will be assuming that our mean is less than or equal to 20, and alternately that it is greater than 20.

00:10 Therefore, we have a one -tail test, and we see that by this alternative.

00:18 This alternative is strictly testing the upper tail, so it's just a one -tail test, and our alpha level is 0 .05.

00:26 So before we even look at the data, oh, well, let's put the data down.

00:30 We know we have a sample size of 36 and they arrived at a mean of 21, but our population standard deviation is said to be 5, which means our sampling distribution of x bar, we're assuming is centered at basically 20, and our standard deviation of our sampling distribution is going to end up being that 5 divided by the square root of 36 or 56.

00:58 And so if we move one standard deviation away, this is 20 and 5, 6, so we can see that this 21 is just a hair bigger up here.

01:10 Now, in our picture, we want to find what the critical value is.

01:17 And because we're using the population standard deviation, it's a z value, and we want that z value to have, we want that z value to end up having all of that point 10.

01:29 In that upper tail and this is where we will reject the null and over this way is where we will fail to reject the null if our mean is over there and this value is a z value the critical value is 1 .645 so there's our critical value and if our test statistic is higher than that we will be rejecting and if it's lower we'll fail to reject so let's find the test statistic so it is a z value and we take the 21 minus the 20 divided by that 5 .6.

02:10 And when we take that, we have one divided by 5 .6, which is going to end up being six -fifths or 1 .2.

02:22 So our test statistic is 1 .2...

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