Question

Consider the hypothesis statement shown below using a = 0.10 and the data to the right from two independent samples. HO: H1 - H220 H1: 1-12 0 a) Calculate the appropriate test statistic and interpret the result. b) Calculate the p-value and interpret the result. Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. X = 114 X2 = 127 6 = 36 02 = 40 n = 50 n = 35 a) The test statistic is (Round to two decimal places as needed.) Determine the appropriate critical value(s). The critical value(s) isare) (Round to two decimal places as needed. Use comma to separate answers as needed.) in the rejection region, Ho. There is evidence to conclude that the mean of population 1 is less than the mean of Since the test statistic population 2 b) The p-value is (Round to three decimal places as needed.) Since the p-value is a, V Ho. There is evidence to conclude that the mean of population 1 is less than the mean of population 2

Answer 1

Part a)

Test Statistic :-
$Z = ( \bar{X}_{1} - \bar{X}_{2}) / \sqrt{(\sigma _{1}^{2} / n1) + (\sigma _{2}^{2}/n2)}$
$Z = ( 114 - 127 ) / \sqrt{( 36^{2} /50 ) + ( 40^{2}/35 )}$
Z = -1.54

Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z( 0.1 ) = 1.28

Z < - 1.28

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z( 0.1 ) = 1.28
Z < -Z(α) = -1.54 < -1.28
Result :- Reject Null Hypothesis

Test statistic lies in the rejection region, reject H0, there is sufficient evidence to support the claim.

Part b)

P value = P ( Z < 1.54 ) = 0.062

Reject null hypothesis if P value < α = 0.10 level of significance
Since 0.062 < 0.10, hence we reject null hypothesis
Result :- Reject null hypothesis

P value is less than α, reject H0, there is sufficient evidence to support the claim.