Question

P_1

Which of the following is a fundamental difference between the t statistic and a z-score?

A. The t statistic uses the sample mean in place of the population mean.

B. The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n.

C. The t statistic computes the standard error using a sample variance in place of the population variance.

D. All of these are differences between t and z statistics.

P_2

For a single sample t-test, what is the sample variance s² and the estimated standard error s_M for a sample of n = 9 scores with SS = 72?

A. s² =8 and s_M= 3

B. s² = 9 and s_M = 3

C. s²= 3 and s_M = 1

D. s² = 9 and s_M = 1

E. None of the above.

P_3

The results of a hypothesis test with the t-test for a single sample are reported as follows: t(60) = 3.70, p < 05., 2-tailed test Based on this report, how many individuals were in the sample?

A. 120

B. 60

C. 61

D. 59

E. None of the above

Answer 1

(1) option C is correct because for t test, we use the sample standard deviation and sample variance whereas for z test, we always use population standard deviation and variance.

(2) variance = SS/(n-1)

setting the given values,we get variance= 72/(9-1)= 72/8 = 9

And standard error = variance/n = 9/9 = 1

So, option D is correct answer

(3) the degree of freedom for one sample t test is always n-1

So, we have degree of freedom = 60

so, sample size n is given as

60 = n-1

adding 1 on each side, we get

n = 60+1 = 61

so, option C is correct answer