Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

H0: p=0.61 versus H1: p<0.61

n=150, x=84, α=0.05

Is np01−p0≥10​?

Yes - Your Answer is Correct

No

Use technology to find the​ P-value.

​P-value=__?__

​(Round to three decimal places as​ needed.)

Answer 1

H0: Null Hypothesis: p = 0.61

H1: Alternative Hypothesis: p < 0.61

n = Sample Size = 150

= Sample Proportion = 84/150 = 0.56

Requirements of the test:

(i) The Sampling method is Simple Random Sampling

(ii) Each sample point can result in just two possible outcomes

(iii) The sample includes at least 10 successes and 10 failures

(iv) The population size isat least 20 times as big as the sample size

The condition is:

np(1-p) 10.

Here

n = 150

p = 0.61

Substituting, we get:

150 X 0.61 X (1 - 0.61) = 35.685 10.

So,

Condition is satisfied.

SE=

Test statistic is given by:

Z = (0.56 - 0.61)/0.0398

= - 1.2555

Table of Area Under Standard Normal Curve gives area = 0.3962

So,

P - value = 0.5 - 0.3962 = 0.104

So,

Answer is:

0.104