Question

Find test statistic and p-value and make conclusion for MEAN:

x=35, n=200, H_o: p=25%, H1: p<25%, confidence level=0.05

Then find test statistic and p-value and make conclusion for PROPORTION:

x̄=37, s=10.2, n=30, H_o: μ=32, H1:  μ≠32, confidence level=0.01

Now find test statistic and p-value and make conclusion for TWO PROPORTIONS:

x₁ = 6, n₁ = 315, x₂ = 80, n₂ = 320, H_o: p₁ = p_2, HA: p1 < p2, α = 0.1

Answer 1

(1)

H0: p = 0.25

H1: p < 0.25

n = 200

= 35/200 = 0.175

= 0.05

From Table, critical value of Z = - 1.64

Test Statistic is given by:

Since calculated Value of Z= - 2.449 is less than critical value of Z = - 1.64, the difference is significant. Reject null hypothesis.

By Technology,

p - value = 0.0073

Since p - value = 0.0073 is less than alpha = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
The date support the claim that population proportion is less than 0.25.

(2)

H0: = 32

H1: 32

n = 30

= 37

s = 10.2

= 0.01

From Table, critical value of t = 2.756

Test Statistic is given by:

Since calculated Value of t = 2.685 is less than critical value of t = 2.756, the difference is not significant. Fail to reject null hypothesis.

By Technology, p value = 0.0119

Since p value = 0.0119 is greater than alpha = 0.01, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The date do not support the claim that population mean is different from 32.

(3)

H0: p1 = p2

H1: p1 < p2

n1 = 315

1= 6/315 = 0.019

n2 = 320

2 = 80/320 = 0.25

= 0.10

From Table, critical value of Z = - 1.28

Pooled Proportion is given by:

Test Statistic is given by:

Since calculated Value of Z= - 8.504 is less than critical value of Z = - 1.28, the difference is significant. Reject null hypothesis.

By Technology, p value = 0.0000

Since p value = 0.0000 is less than alpha = 0.10, the difference is significant. Reject null hypothesis.

Conclusion:
The date support the claim that p1 < p2.