Question

7.126 Two-sample t test versus matched pairs t test. Consider the following data inspections are available through its online newspaper. patrons at risk of getting sick and must immediately be corrected by the restaurant. An SRS of n = 200 inspections from the more than 16,000 inspections since January 2012 were collected, resulting in x ̄=0.995 violations and s = 1.822 violations. Critical food violations are those that put set. The data were actually collected in pairs, and each row represents a pair. Group1 Group2 48.86 48.88 50.60 52.63 51.02 52.55 47.99 50.94 54.20 53.02 50.66 50.66 45.91 47.78 48.79 48.44 47.76 48.92 51.13 51.63 PAIRED (a) Suppose that we ignore the fact that the data were collected in pairs and mistakenly treat this as a two-sample problem. Compute the sample mean and variance for each group. Then compute the two-sample t statistic, degrees of freedom, and P-value for the two-sided alternative. (b) Now analyze the data in the proper way. Compute the sample mean and variance of the differences. Then compute the t statistic, degrees of freedom, and P-value. (c) Describe the differences in the two test results.

Answer 1

(a)

Group1	Group2
49.6920	50.5450	mean
2.3179	1.9244	std. dev.
10	10	n
	18	df
	-0.85300	difference (Group1 - Group2)
	4.53790	pooled variance
	2.13023	pooled std. dev.
	0.95267	standard error of difference
	0	hypothesized difference
	-0.895	t
	.3824	p-value (two-tailed)

(b)

49.69200	mean Group1
50.54500	mean Group2
-0.85300	mean difference (Group1 - Group2)
1.26912	std. dev.
0.40133	std. error
10	n
9	df
-2.125	t
.0625	p-value (two-tailed)

(c) In part (a), we considered that the data has equal variance and the groups are independent. In part (b), we assume that the data is paired. So, that's why we have obtained different results.