Question

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

Upper H0​:

pequals=0.8

versus

Upper 1H :p

greater than>0.80

nequals=250

xequals=205

alphaαequals=0.05

Is

np 0 left parenthesis 1 minus p 0 right parenthesisnp01−p0greater than or equals≥​10?

Use technology to find the​ P-value.

​P-valueequals=nothing

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

Answer 1

Here we have to test the

Ho : P = 0.80 vs H1 : P > 0.80

n = 250 , x = 205

npo = 250*0.80 = 200 and n*Po*(1-po) = 40

So n*po and n*Po*(1-po) 10

Test statistic Z

Z = p^ - P /sqrt(P*(1-P)/n)

Where p^ = 205/250 = 0.82

Z = 0.82 - 0.80/sqrt( 0.80*0.20)/250))

Z = 0.79

P value using technology

P value = P ( Z > 0.79)

P-value = 0.215

Test criteria : if p value    we reject Ho , otherwise we fail to reject Ho

P-value = 0.215 > 0.05

We fail to reject Ho