Question

46.1 55.2 517 47.7 54.5 53.6 46.7 51. 9 47.0 48.6 41.5 452 52.1 51.0 54.5 -1.9 -52 -1.6 -3.7 -3.5 -13 -1.6 0.7 (Type integers or decimals.) (b) Computed and sa d = -2.263 (Round to three decimal places as needed.) Sg = 1.810 (Round to three decimal places as needed.) (c) Test if He <0 at the a= 0.05 level of significance What are the correct null and alternative hypotheses? B. Ho H0 A. Ho Ha=0 H, 1. 0 Hi Ho = 0 Ho Hd > 0 C C Ho Pa 0 H, μ. Ο Hi Hd <0 P-value (Round to three decimal places as needed Enter your answer in the answer box and then click Check Answer Clear All 2 Pemaining

Answer 1

a)

Xi	46.1	55.2	51.7	46.7	47	41.5	51	52.1
Yi	47.7	54.5	53.6	51.9	48.6	45.2	54.5	53.4
di	-1.6	0.7	-1.9	-5.2	-1.6	-3.7	-3.5	-1.3b)

b) From the given information,

Sample mean of differences = -2.263

Sample standard deviation of differences s_d = 1.810

Sample size (n) = 8

c)

H₀ : μ_d = 0

H₁: μ_d < 0

This is a left - tailed test.

The test statistics t = ( - μ_d) / (s_d / √n)

t = ( -2.263 - 0)/(1.810/sqrt(8)) = -3.5363

Test statistics t = -3.5363

Using excel function, P value = T.DIST(-3.5363,7,TRUE)= 0.0048

P- value = 0.0048

The p-value is less than α = 0.05 so we can reject null hypothesis.

This test statistics lead to a decision to reject the null hypothesis at 0.05 level of significance.