Question

Assume that both populations are normally distributed. a) Test whether 147 *H2 at the a=0.10 level of significance for the given sample data. b) Construct a 90% confidence interval about 17 - H2 Sample 1 18 19.1 5.1 Sample 18 20.3 4.8 Click the icon to view the Student t-distribution table. a) Perform a hypothesis test. Determine the null and alternative hypotheses. O A. Ho H1 H2 H H1 H2 OB. Ho: H = H2, H:Hy * H2 OC. Ho: H = H2, H:<H2 OD. Hoi Hy #H2, H H1 H2 Determine the test statistic. t(Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) O A. The critical value is. OB. The lower critical value is The upper critical value is Should the hypothesis be rejected? the null hypothesis because the test statistic the critical region. b) Construct a 90% confidence interval about H1 H2 The confidence interval is the range from to (Round to two decimal places as needed. Use ascending order.)

Answer 1

Answer:

a)

Given,

Ho : u1 - u2 = 0

Ha : u1 - u2 != 0

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

substitute values

= sqrt(((18-1)5.1^2 + (18-1)4.8^2)/(18+18-2))

= 4.95

test statistic = (x1 - x2)/Sp*sqrt(1/n1 + 1/n2)

substitute values

= (19.1 - 20.3)/4.95*sqrt(1/18 + 1/18)

= - 0.73

P value = 0.47039

Here p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.

b)

degree of freedom = n1 + n2 - 2 = 34

alpha = 0.1

t = 1.690924

CI = (x1-x2) +/- Sp*t*sqrt(1/n1 + 1/n2)

= (19.1 - 20.3) +/- 4.95*1.69*sqrt(1/18 + 1/18)

= - 1.2 +/- 2.7885

= (-3.9885 , 1.5885)