Q: Use hypothesis testing procedures to test the a priori assumption that people who are fearful of walking in their neighborhood at night have lower average trust than people who are not fearful. Use a 2 t-tail, with alpha of 0.001
Fear
Yes No
Mean 1.08 1.46
S.D 1.14 1.14
n 245 415
My work:
t= 1.08-1.46/sqrt 1.14^2/245 + 1.14^2/415 = -4.14
Can t-statistics be negative? Am I doing something wrong?
The t-statistic can indeed be negative. In hypothesis testing, the sign of the t-statistic indicates the direction of the difference between the sample means.
However, there seems to be a mistake in your calculation. The formula for the t-statistic is:
t = (Mean1 - Mean2) / sqrt[(SD1^2 / n1) + (SD2^2 / n2)]
Let's calculate the t-statistic correctly:
Mean1 = 1.08
Mean2 = 1.46
SD1 = 1.14
SD2 = 1.14
n1 = 245
n2 = 415
t = (1.08 - 1.46) / sqrt[(1.14^2 / 245) + (1.14^2 / 415)]
= -0.38 / sqrt[0.005878 + 0.003259]
= -0.38 / sqrt(0.009137)
= -0.38 / 0.095647
= -3.970
The t-statistic is approximately -3.970, which represents the standardized difference between the means of the two groups.
This means that the calculated t-value is -3.970, which is the test statistic that we will use to compare to the critical value to make a decision.
To continue with hypothesis testing, you will need to determine the critical value for a two-tailed test with an alpha level of 0.001 and the degrees of freedom, which can be calculated as df = n1 + n2 - 2.
Once you have the critical value, compare it to the absolute value of the t-statistic (-3.970) and make a decision based on whether the absolute value of the t-statistic exceeds the critical value.
Remember that hypothesis testing involves steps beyond just calculating the t-statistic, such as setting up the null and alternative hypotheses and determining the critical region.