Question

Need help figuring out how the P value was obtained, can I please get a breakdown of the process?

Population1 Population 2 Assume that both populations are normally distributed (a) Test whether ?1 12 at the ?:0.05 level of significance for the given sample data. (b) Construct a 95% confidence interval about 1- 16 5.6 (a) Test whether ?| 2 at the ? 0.05 level of significance for the given sample data. Determine the null and alternative hypothesis for this test. Detemine the P-value for this hypothesis test. P0.48 Round to three decimal places as needed.) Should the null hypothesis be rejected? A. Do not rejeat Ho. there is not sufficient evidence to conclude that the two populations have different means OB. Do not reject Ho. there is sufficient evidence to conclude that the two populations have different means. OC. Reject Ho. there is sufficient evidence to conclude that the two populations have different means OD. Reject Ho. there is not sufficient evidence to conclude that the two populations have different means. (b) Construct a 95% confidence interval about ?1-?2 -2.68.5.28) Round to two decimal places as needed.)

Answer 1

The test statistic t = ( $\bar x1 - \bar x2$ )/sqrt(s1^2/n1 + s2^2/n2)

                             = (19.2 - 17.9)/sqrt((4.5)^2/15 + (5.6)^2/15)

                             = 0.7008

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

      = ((4.5)^2/15 + (5.6)^2/15)^2/(((4.5)^2/15)^2/14 + ((5.6)^2/15)^2/14)

      = 27

P-value = 2 * P(T > 0.7008)

             = 2 * (1 - P(T < 0.7008))

             = 2 * (1 - 0.7553)

            = 0.489