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A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. 

  Proctored Nonproctored
mu u1 u2
n 35 31
X_bar 76.94 83.52
s 10.87 21.94

a. Test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. What are the null and alternative hypotheses?

What are the null and alternative hypothesis?

The test statistic, t is ?

The P-value 

state the conclusion for the test. 

t-test assuming that the population standard deviations are not equal. 

I used Minitab to solve this and the output is presented below. 


Two-Sample T-Test and CI 

Sample   N  Mean  StDev  SE Mean
1       35  76.9   10.9      1.8
2       31  83.5   21.9      3.9

Difference = μ (1) - μ (2)
Estimate for difference:  -6.58
95% upper bound for difference:  0.73
T-Test of difference = 0 (vs <): T-Value = -1.51  P-Value = 0.069  DF = 42


The null hypothesis would not be rejected at the 0.05 level of significance because p = 0.069 is greater than alpha. 

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