Assume that the differences are normally distributed. Complete parts (a) through (d) below.
Observation 1 2 3 4 5 6 7 8
Xi 49.3 54.9 45.5 49.1 48.7 50.4 47.9 53.5
Yi 52.9 54.7 48.2 54.2 48.5 53.5 52.6 53.3
(a) Determine di = Xi - Yi for each pair of data.
Observation 1 2 3 4 5 6 7 8
di
(Type integers or decimals.)
(b) Compute d̄ and sd.
d̄ = (Round to three decimal places as needed.)
sd = (Round to three decimal places as needed.)
(c) Test if μd < 0 at the α = 0.05 level of significance.
What are the correct null and alternative hypotheses?
A. H0: μd < 0, H1: μd = 0
B. H0: μd < 0, H1: μd > 0
C. H0: μd = 0, H1: μd < 0
D. H0: μd > 0, H1: μd < 0
P-value = (Round to three decimal places as needed.)
Choose the correct conclusion below.
A. Do not reject the null hypothesis. There is sufficient evidence that μd < 0 at the α = 0.05 level of significance.
B. Reject the null hypothesis. There is sufficient evidence that μd < 0 at the α = 0.05 level of significance.
C. Reject the null hypothesis. There is insufficient evidence that μd < 0 at the α = 0.05 level of significance.
D. Do not reject the null hypothesis. There is insufficient evidence that μd < 0 at the α = 0.05 level of significance.
(d) Compute a 95% confidence interval about the population mean difference μd.
The lower bound is .
The upper bound is .
(Round to two decimal places as needed.)