Question

As a follow up to the analysis of his Stats classes, Dr. Walton wants to assess if the move to fully online learning as a result of the COVID-19 pandemic impacted student learning in his Research Methods class in anyway (i.e., either increased or decreased student learning). To do so he conducts a TWO-TAILED Z-test using a standardized Research Methods quiz. He compares his students’ scores (N = 27: x̅ = 83.5%) with the national average of scores on the same quiz (µ = 80.8%: σ = 6.2).

Write in words, Dr. Walton’s alternative hypothesis (remember, it is TWO-TAILED so we are testing for a difference in ANY direction) .

Write in words, the Null-hypothesis .

The Standard Error of the Mean for the sampling distribution of means is . Round to three decimal places (.XXX)

The z score for the sample mean of Dr. Walton’s students Stats test scores is . Round to two decimal places (.XX).  

What is the Critical Z-value for a Two-Tailed Z-test with an alpha .05 criterion . Round to two decimal places (.XX)

Is the sample mean of Dr. Walton’s students’ test score in the region of rejection?  

Will you reject the Null-Hypothesis?

Do Dr. Walton’s Students’ scores on the standardized research methods quiz appear to be significantly different than the national average on this quiz and what is your evidence?

Answer 1

Solution:

Given:

Sample size = n= 27

Sample mean = x̅ = 83.5%

The national average of scores on the same quiz : µ = 80.8% and σ = 6.2

Dr. Walton wants  to test if move to the fully online learning as a result of the COVID-19 pandemic impacted student learning in his Research Methods class in anyway.

Part a) Write in words, Dr. Walton’s alternative hypothesis

H_a: Move to the fully online learning as a result of the COVID-19 pandemic impacted student learning in his Research Methods class in anyway

That is:

Dr. Walton’s Students’ scores on the standardized research methods quiz appear to be significantly different than the national average on this quiz.

Part b) Write in words, the Null-hypothesis .

H0: Move to the fully online learning as a result of the COVID-19 pandemic DOES NOT impacted student learning in his Research Methods class in anyway

that is:

Dr. Walton’s Students’ scores on the standardized research methods quiz does not appear to be significantly different than the national average on this quiz.

Part c) The Standard Error of the Mean for the sampling distribution of means

Part d) The z score for the sample mean of Dr. Walton’s students Stats test scores

Part e) What is the Critical Z-value for a Two-Tailed Z-test with an alpha .05 criterion .

Since this is two tailed, we find : Area =

Look in z table for area = 0.0250 or its closest area and find z value

Area 0.0250 corresponds to -1.9 and 0.06

thus z critical value = -1.96

Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96)

Part f) Is the sample mean of Dr. Walton’s students’ test score in the region of rejection?  

Since z test statistic value = > 1.96, the sample mean of Dr. Walton’s students’ test score is in the region of rejection.

Part g) Will you reject the Null-Hypothesis?

Yes. Since the sample mean of Dr. Walton’s students’ test score is in the region of rejection.

Part h) Do Dr. Walton’s Students’ scores on the standardized research methods quiz appear to be significantly different than the national average on this quiz and what is your evidence?

Yes. Since we have rejected null hypothesis.