Consider the following hypothesis test: H0: μ≤ 25 Ha: μ >...

Consider the following hypothesis test: $H_0: \mu \leq 25$ $H_a: \mu > 25$ A sample of 40 provided a sample mean of 26.4 and sample standard deviation of 6. a. Compute the value of the test statistic. b. What is the p-value? Provide a range if you cannot calculate an exact value. c. At $\alpha = 0.01$, what is your conclusion? d. What is the rejection rule using the critical value? What is your conclusion?

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00:01 So in this problem, we are given that our null hypothesis is that our mu is less than or equal to 25.

00:08 Our alternative hypothesis is that our mu is greater than 25.

00:13 Our population mean is greater than 25.

00:16 It also gives us that our n, our sample, is equal to 40.

00:21 Our sample mean, our x bar, is equal to 26 .4.

00:29 Our population standard deviation is equal to six, and that's all we need.

00:36 So the first thing we need to do is find a test statistic.

00:41 So for us in this problem, we will use a z score, and in order to compute a z score, we will take the sample mean and subtract the population mean from it, and divided by the population standard deviation divided by the square root of n.

01:07 So for us, that is equal to 26 .4 minus 25 over 6 divided by the square root of 40.

01:21 So once we do all the math, we get that our z is equal to approximately 1 .48.

01:31 8.

01:32 Now, what do we do with that z value? we are supposed to find the p value.

01:38 So, what is a p value? the p value is the area under the curb representing the probability associated with the z value.

01:45 Now, because our alternative hypothesis, our alternative, our alternative hypothesis is that our mu is greater than 25.

01:56 We know this is a right -tailed z test.

02:00 Our z is going to be somewhere over there...

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