Question

please solve and highlight answers

Calculate the test statistic and p-value for each sample. Use Appendix C-2 to calculate the p-value. (Negative values should be Ind icated by a minus sign. Round your test statistic to 3 decimal places and p-value to 4 decimal places.) Test Statistic p-value (a) Ho: 0.50 versus H: T0.50, a 0.05, x= 48. n 81 (b) Ho: T 0.30 versus H: T # 0.30, a 0.05, x 18, n 39 (c) Ho: 0.10 versus H: <0.10, a 0.01, x 6, n 109

Answer 1

a) Given that,

H0 : π ≤ 0.50 versus H1 : π > 0.50

x = 48, n = 81

sample proportion $(\hat p)$ = 48/81 = 0.5926

Test statistic is,

Z = 0.5926 - 0.50 0.50*(1-0.50) == 1.667 2 - pon. 10:30 1.66

=> Test statistic = 1.667

p-value = P(Z > 1.667) = 0.0478

=> p-value = 0.0478

b) Given that,

H0 : π = 0.30 versus H1 : π ≠ 0.30

x = 18, n = 39

sample proportion $(\hat p)$ = 18/39 = 0.4615

Test statistic is,

Z = 0.4615 - 0.30 0.30+(1-0.30) = 2.201 39

=> Test statistic = 2.201

p-value = 2 * P(Z > 2.201) = 2 * 0.0139 = 0.0278

=> p-value = 0.0278

c) Given that,

H0 : π ≥ 0.10 versus H1 : π < 0.10

x = 6, n = 109

sample proportion $(\hat p)$ = 6/109 = 0.0550

Test statistic is,

Z = 0.0550 - 0.10 0.10*(1-0.10) 109 == -1.564 7/ 01 10 -1.564

=> Test statistic = -1.564

p-value = P(Z < -1.564) = 0.0589

=> p-value = 0.0589