A professor wants to know whether male and female psychology students have diffe

Question

A professor wants to know whether male and female psychology students have different GPA. He surveyed the students in his statistics class and obtained the following data: Male Female n_1 = 9 n_2 = 19 M_1 = 3.14 M_2 = 3.09 S_1 = 100 S_2 = 247 State the hypotheses. Should the alternative hypothesis be directional or Determine the critical t for alpha= .05 (Appendix C. t Table). Mark the critical value of t, the region of rejection, and region of retention. Calculate the t (show your steps, start from the equation). Compare your results with the SPSS output. Calculate the pooled variance Calculate the standard error of the difference between two sample means Calculate the t Interpret the result. Can you reject the null hypothesis? What is your conclusion regarding the alternative hypothesis? Conduct an independent-samples t test on the survey data, verify the result of your manual calculations, and report your findings. The SPSS output should be inserted into your WORD file or submitted as a separate file. SPSS data file:. You will need two variables for the t test: Q2gender, Q7GPA. Menu steps Analyze Compare Means A Independent-Samples T test; Test Variable (s): DV Grouping Variable: IV, Define Groups (1, 2), Continue; OK (for the SPSS procedures also see the video posted on à in-class activities)

Explanation / Answer

( a. )

Null Hypothesis and Alternative Hypothesis:

H0: µ1 = µ2

H1: µ1 ¹ µ2

This is a two-tailed test. Here the alternative hypothesis is non-directional.

( b. )

Here the degrees of freedom = n1 + n2 – 2 = 9 + 19 – 2 = 26. The level of significance is .05.

From the critical table we get the critical values are -2.056 and + 2.056.

The rejection regions are t <= -2.056 and t >= 2.056

The region of retention is -2.056 < t < 2.056

( c. )

Pooled variance = ((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2)

n1 = 9 , n2 = 19, s1 = 1.09 and s2 = 2.47

Pooled variance = 4.5893

Standard Error = ((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2) * (1/n1+1/n2)

Standard error = 0.8669

t = (3.14 – 3.09)/ 0.8669

= 0.058

( d.) The value of the test statistics falls in retention region. We are fail to reject the null hypothesis. We are going to reject the alternative hypothesis.

At 5% level of significance there is not sufficient evidence to conclude that male and female psychology student have different GPA.

Note: SPSS result is not available here, so unable to compare with SPSS.

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