Question

Chapter 7 - Sampling Distribution

6. A normal population has a = 50 and = 8. A random sample is taken form this population (n = 16) and has its own M = 54. What is the z score for this sample mean (M)? (Distribution of sample means)

Chapter 8 – Introduction to Hypothesis Testing

7. Identify the four steps of hypothesis test as presented in this chapter.

8. Define the alpha level and the critical region for a hypothesis test.

9. Define Type I and Type II errors.

10. A university president believes that, over the past few years, the average age of students attending his university has changed. To test this hypothesis, an experiment is conducted in which the age of 150 students who have been randomly sampled from the student body is measured. The mean age is 23.5 years. A complete census taken at the university a few years before the experiment showed a mean age of 22.4 years, with a standard deviation of 7.6.

(Hypothesis test statistic for a single sample; population known – z scores)

Answer 1

6.

Given

Sample Size, n = 16

For M = 54, the z-score is calculated as

7.

The four steps of hypothesis are

1. Nature of the population distribution and the parameters of interest

2. Setting up of Null Hypothesis (H0) and the Alternative Hypothesis (H1) in terms of the range of the parameter values each one embodies

3. Choose and compute the appropriate test statistic

4. Partitioning the set of possible values of the test statistic into two disjoint sets Rejection or Critical Region and Acceptance Region and draw inference considering the test statistic , rejection region

8.

Alpha level:

An alpha level is probability of type I error i.e., probability of rejecting null hypothesis (H0) when the null hypothesis (H0) is true

Critical Region of a Hypothesis test:

The region of rejection of null hypothesis (H0) when H0 is true is that region of the outcome set where H0 is rejected if the sample point falls in that region and is called critical region

9.

Type I error: Error of rejecting null hypothesis (H0) when H0 is true

Type II error: Error of accepting null hypothesis (H0) when H0 is false

10.

Given

Sample size, n = 150

To test

Null Hypothesis (H0) :

versus

Alternative Hypothesis (H1) :

The z test statistic under H0 for single sample is

Z critical value for two tail test at 5% level of significance, Z = 1.96

Since the calculated z (=1.7727) < Z (=1.96) as 5% level of significance, we do not reject the null hypothesis (H0) and infer that the mean age of the students attending his university is 22.4 years