Question

14. Explain the possible consequences of not using the degrees of freedom when calculating the sample standard deviation?

16. A researcher tested two groups (females and males) of rats on memory performance. The following scores are for the number of correct choices they made on the task:

Females       Males
9                    8
7                    6
7                    8
8                    6
9                    7
8                    6
9                    9
9                    6

Calculate the standard deviation for each group.
Which group shows more variability in their memory scores?         

18. Using the Empirical Rule how much of the population is found in the 1st, 2^nd and 3^rd standard deviation?

Answer 1

14. T-tests are hypothesis tests for the mean and use the t-distribution to determine statistical significance.

A 1-sample t-test determines whether the difference between the sample mean and the null hypothesis value is statistically significant. We know that when you have a sample and estimate the mean, you have n – 1 degree of freedom, where n is the sample size. Consequently, for a 1-sample t-test, the degrees of freedom is n – 1.

The DF defines the shape of the t-distribution that your t-test uses to calculate the p-value. Because the degrees of freedom are so closely related to sample size, you can see the effect of sample size. As the degrees of freedom decreases, the t-distribution has thicker tails. This property allows for the greater uncertainty associated with small sample sizes.

16.

	Females	Males
	9	8
	7	6
	7	8
	8	6
	9	7
	8	6
	9	9
	9	6
Standard deviation	0.886405	1.195229

Males show more variability in their memory scores.

18. 1st standard deviation =  68%

2nd standard deviation = 95%

3rd standard deviation = 99%