Hypothesis Testing

APP6JMaloney problems 2. 4, 6, 10, 18, 22, 24

2 ) The value of the z score un a hypothesis test is influenced by a variety of factors.

Assuming that all the other variables are held constant, explain how the value

of Z is influenced by each of the following?

Z= M - u / SD

a) Increasing the difference between the sample mean and the original.

The z score represents the distance of each X or score from the mean.

If the distance between the sample mean and the population mean the z score will

increase.

b) Increasing the population standard deviation.

The standard deviation is the factor that is used to divide by in the equation. the bigger the SD,

then the smaller the z score.

c) Increasing the number of scores in the sample.

Should bring the samples mean closer to the population mean so z score will get smaller.

4) If the alpha level is changed from .05 to .01

a) what happens to the boundaries for the critical region?

It reduces the power of the test to prove the hypothesis.

You increase the chance of rejecting a true H

b) what happens to the probability of a type 1 error?

Type 1 error is falsely reporting a hypothesis,

Where you increase the chance that you will reject a true null hypothesis.

6) A researcher is investigating the effectiveness of a new study skills training program for elementary

school childreen. A sample of n=25 third grade children is selected to participate in the program

and each child is given a standardizrd achievement test at the end of year. For the regular

population of third grade children, scores on the test form a normal distribution with a

mean u = 150, and a standard deviation q = 25. The mean for the sample is M = 158.

a) Identify the independent and the dependent variables in the study

Independent = third grade child

Dependent = Score on test

b) Assuming a two-tailed test, state null hypothesis that includes the independent & dependent variable.

Ho: After the program the mean will still be 150

H1: After the program the mean will be different from 150

c) Using symbols, state the hypotheses (H and H) for the two tailed test.

Ho: u=150

H1: μ ≠150

d) Sketch the appropriate distribution, and locate the critical region for u=.05

Put 150 instead of 50 for u

e) Calculate the test statistic (z-score) for the sample

qm = q / square root of number in sanple = 25 / sq root of 25 = 25 / 5 = 5

Z= M - u / qm = 158 - 150 / 5 = 8 / 5 = 1.6

f) what decision should be made about the null hypothesis, & the effects of the program?

- a statistical decision about the Null hypothesis.

- and a conclusion about the outcome of the experiment.

10) State college is evaluating a new English composition course for freshman.

A random sample of n=25 freshman is obtained and the students are placed

in the course during their first semester. One year later, a writing sample is obtained

for student and the writing samples are graded using a standardized evaluation

technique. The average score for the sample is M=76. For the general population

of college students, writing scores from a normal distribution with a mean of u=70.

a) If the writing scores for the population have a standard deviation of q=20, does the sample

provide enough evidence to conclude that the new composition course has a

significant effect? Assume a two-tailed test with alpha = .05

I need to find the z score...

q for the population = q for the sample / sq root of number in sample =

Therefore = 20 / sq root of 25 = 20/5 = 4 is the q for population

Z = M - u / 4

76 - 70 / 4 = 6 / 4 = 1.5 is the z score

No the sample does not, the z score was only 1.5, you need at least 1.96 (pos or neg)

b) If the population standard deviation is q=10, is the sample sufficient to demonstrate a

significant effect? Again, assume a two-tailed test with alpha=.05

I need to find the z score...

q for the population = q for the sample / sq root

...