Two groups of 50 college students from different institution

Two groups of 50 college students from different institutions are administered the test. The mean score of the first group was 55, with a standard deviation of 6. The mean score of the second group was 64, with a standard deviation of 5.

1) What statistical test (t-statistic) would you use to evaluate the data and why?

2) Can a researcher conlcude that the resilience scores of students at the second institution are different from those at the first? Please define the critical region, do the test, and state the directional hypothesis.

**I believe this is an independent measures t-test, but I keep getting huge t-statistic values. I\'m not sure if this is relevant, but on the page before (for different questions) it says that the test is out of 100 pts, with normally distributed scores with a mean of 65 and a standard deviation of 12.

Solution

1) Paired t test can be conducted for this

H0: mu1 = mu2

Ha: mu1 not equals mu2

mu1-mu2 = 55-64 = -9

The mean of Group One minus Group Two equals -9.00
  95% confidence interval of this difference: From -23.31 to 5.31

t = 1.2481
  df = 98

  standard error of difference = 7.211

The two-tailed P value equals 0.2150
  By conventional criteria, this difference is considered to be not statistically significant.