Question

Edit question In the following research, identify 1. test type, 2. null hypothesis, 3. alternate hypothesis, 4. test statistic, 5. p-value, and 6. conclusion.

A researcher took a sample of the grade point averages for students in his class. For 25 students, the standard deviation of grade points was 0.65, and the mean was 2.89. In the previous semester his class had an average of 2.95. Is there evidence that his current class is significantly different from his previous class?

Test type:	Example: 2-sided, 1 sample t-test
Null hypothesis:	Example: mean finger length on right hand is 20.6 OR µ(finger length) = 20.6
Alt hypothesis:	Example: mean finger length on right hand is >20.6 OR µ(finger length) > 20.6
Test-statistic (t):	#
p-value:	#
Conclusion:	Conclusions should interpret the test-statistic (sig/not sig), make a statement about the hypotheses (reject/fail to reject) and answer the research question.

Answer 1

We have given that,

Sample mean xbar = 2.89, sample standard deviation = 0.65, sample size n = 25.

Population mean μ = 2.95.

We want to test the claim that his current class is significantly different from his previous class.

So this test is two sided test.

Here we are conducting t test because population standard deviation is unknown.

1. Test type: Two - sided one sample t test

2. Null hypothesis: μ= 2.95
3. Alternative hypothesis: μ ≠ 2.95

This is two sided test.

4. Test statistics:

t = (xbar – μ) / (s/√n) = (2.89 – 2.95)/(0.65/sqrt(25)) = -0.462

Test statistics (t) = -0.462

5. P-value = T.DIST.2T(0.462,24)= 0.648………. (Using Excel function)

P-value = 0.648

Decision: Fail to reject H₀ because the P- value is greater than the 5% significant level.

6. Conclusion: We fail to reject null hypothesis. There is not sufficient evidence to claim that his current class is significantly different from his previous class at 5% level of significance,