Question

Calculate the test statistic and p-value for each sample. Use Appendix C-2 to calculate the p-value. (Negative values should be indicated by a minus sign. Round your test statistic to 2 decimal places and p-value to 4 decimal places.)

	Test Statistic	p-value
(a) H0: ππ ≤ .60 versus H1: ππ > .60, α = .05, x = 56, n = 80
(b) H0: ππ = .30 versus H1: ππ ≠ .30, α = .05, x = 18, n = 40
(c) H0: ππ ≥ .10 versus H1: ππ < .10, α = .01, x = 3, n = 100

Answer 1

a)

Sample proportion $\hat{p}$ = 56 / 80 = 0.70

Test statistics

z = ($\hat{p}$ - p) / sqrt [ p( 1 - p) / n ]

= (0.7 - 0.6 ) / sqrt [ 0.6 * 0.4 / 80 ]

= 1.83

p-value = P(Z > z)

= P(Z > 1.83)

= 0.0336

b)

Sample proportion $\hat{p}$ = 18 / 40 = 0.45

Test statistics

z = ($\hat{p}$ - p) / sqrt [ p( 1 - p) / n ]

= (0.3 - 0.45 ) / sqrt [ 0.3 * 0.7 / 40 ]

= -2.07

p-value = 2 * P(Z < z)

= 2 * P(Z < 2.07)

= 0.0384

c)

Sample proportion $\hat{p}$ = 3 / 100 = 0.03

Test statistics

z = ($\hat{p}$ - p) / sqrt [ p( 1 - p) / n ]

= (0.03 - 0.10 ) / sqrt [ 0.1 * 0.9 / 100 ]

= -2.33

p-value = P(Z < z)

= P(Z < -2.33 )

= 0.0099