Repeat Exercise 10.15 for samples of size n= 25. Use the same critical region.

Name: Problem 16, Chapter 10: Probability & statistics for engineers & scientists
Uploaded: 2021-12-16T04:05:06-08:00
Duration: 3 min 29 s
Channel: Jameson Kuper
Description: Repeat Exercise 10.15 for samples of size n= 25. Use the same critical region.

Repeat Exercise 10.15 for samples of size n= 25. Use the...

Key Concepts

Significance Level

A predetermined threshold for the probability of committing a Type I error—that is, rejecting the null hypothesis when it is true. It sets the level of risk deemed acceptable for making such an error and plays a key role in defining the critical region.

Test Statistic

A numerical summary of the sample data that is used to evaluate the truth of the null hypothesis. It is compared against the critical values obtained from the relevant probability distribution to determine whether the null hypothesis can be rejected.

Sample Size

The number of observations or data points included in a statistical sample. Sample size affects the precision of estimations, the variability of test statistics, and the overall power of hypothesis tests, with larger samples generally leading to more reliable inferences.

Hypothesis Testing

A statistical method used to decide whether there is enough evidence in a sample to infer that a certain condition holds for the entire population. It involves comparing a test statistic to a threshold (critical region) derived from the null hypothesis, and making decisions based on the probability of observing the sample data under that hypothesis.

Critical Region

The set of all outcomes which cause the rejection of the null hypothesis. It is determined based on the significance level of the test and defines the threshold values for the test statistic—the values that lead to a conclusion that the observed sample is unlikely under the null hypothesis.

Transcript

00:01 Here's the solution to number 16, and we're basically just going to repeat number 15 with this information, but this time the sample size changed.

00:07 So a lot of this is basically the exact same logic.

00:14 So to find alpha, that's the probability of a type 1 error, which means we're going to reject h .0 whenever h .0 is actually true.

00:20 So that means we're going to find the probability that x bar is less than or equal to 191, or the x bar is greater and equal.

00:30 To 209, given that, mu in fact, equals 200.

00:35 So basically the same thing.

00:38 We're just going to do, so mu is 200.

00:41 It's supposed to be in the middle.

00:43 191, and then here's 209.

00:47 So we're going to shade to the left and to the right.

00:50 So we're finding those probabilities.

00:51 So we're going to do the normal cdf.

00:53 I'm just going to do cdf.

00:54 So normal cdf, where the lower bound is negative infinity, the upper bound is 191.

01:00 The mean is 200, and the standard deviation this time is the 15 divided by a square root of 25.

01:09 So that actually is a smaller standard deviation is 3.

01:12 And we're going to add that to the cdf of 209 being the lower bound, infinity being the upper bound.

01:19 The mean is 200, and the standard deviation is also 3.

01:23 15 divided by a square root of 25, so 15 over 5 is 3...

Please give Ace some feedback