Question

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

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

Upper H 0H0​:

pequals=0.40.4

versus

Upper H 1H1​:

pgreater than>0.40.4

nequals=125125​;

xequals=6060​;

alphaαequals=0.010.01

Calculate the test​ statistic,

z 0z0.

z 0z0equals=nothing

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

SOLUTION:

From given data,

Test the hypothesis using the​ P-value approach.

H0​ : p = 0.4

H1 ​:  p > 0.4

n = 125

x = 60

α =0.01

Sample proportion = x / n

= 60 / 125

= 0.48

Test statistics

z0 = - p / = 0.48 - 0.4 / = 0.08 / 0.0438178

= 1.82 ​(Round to two decimal places as​ needed.)

This is test statistics value.

p-value for right tailed test is

p = P( Z > z0)

= P( Z > 1.82)

= 1 - P( Z < 1.82)

= 1 - 0.9656

= 0.0344

Since p-value > 0.01 level, we do not have sufficient evidence to reject H0.

We conclude that,

Do not reject the null hypothesis because p-value is greater than α .

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