Question

Research Scenario B: a teacher gives a reading skills test to a third-grade class of n = 23 at the beginning of the school year. To evaluate whether students changed over the course of the year, they are tested again at the end of the year. Their test scores showed an average improvement of M_D = 5.3 points with s² = 75.

Is this a one-tailed or two-tailed test?

		One-tailed test
		Two-tailed test

Continuing with Scenario B (from Question #17), if the teacher decides to test at the alpha = .01 level, what are the degrees of freedom and critical t value?

		df = 22, critical t = +/-2.82
		df = 24, critical t = 2.49
		df = 27, critical t = 2.47
		df = 22, critical t = +/-2.07

Continuing with Scenario B, given the observed t-statistic, should the teacher reject or retain the null hypothesis (H₀)?

Continuing with Scenario B (from Question #17): a teacher gives a reading skills test to a third-grade class of n = 23 at the beginning of the school year. To evaluate whether students changed over the course of the year, they are tested again at the end of the year. Their test scores showed an average improvement of M_D = 5.3 points with s² = 75.

Construct a 99% confidence interval for the mean difference to estimate the population mean difference.

		0.30 to 10.30
		1.32 to 9.44
		-1.05 to 8.67
		3.61 to 10.13

Answer 1

Two-tailed test

17)

df = 22, critical t = +/-2.82

18)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (5.3 - 0)/(8.6603/sqrt(23))
t = 2.935

Reject H0

19)

sample mean, xbar = 5.3
sample standard deviation, s = 8.66
sample size, n = 23
degrees of freedom, df = n - 1 = 22

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.82

ME = tc * s/sqrt(n)
ME = 2.82 * 8.66/sqrt(23)
ME = 5.092

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (5.3 - 2.82 * 8.66/sqrt(23) , 5.3 + 2.82 * 8.66/sqrt(23))
CI = (0.30 , 10.30)