Question

Nex is a medicine that can be used to reduce the acid produced by the body and heals damage to the esophagus due to acid reflux. The manufacturer of Nex claims that over 94% of patients taking Nex are cured in 8 weeks. In clinical trials, 214 of 225 patients suffering from acid reflux disease were cured after 8 weeks. Test the manufacturer's claim at the significance level α = 0.05.

Hypothesis test H0: Versus H1:

Using the p value method, the test statistical is?

The P value is?

What is the decision?

What is the conclusion?

Answer 1

The manufacturer of Nex claims that over 94% of patients taking Nex are cured in 8 weeks.

We write the hypothesis as

H0: p = 0.94   Vs H1 : p > 0.94   ( we select > sign for H1 because over means More than )

n = sample size = 225

x = 214

Formula for test statistics

Test statistics = 0.701793268

p value = P ( Z < 0.701793268 )

Beacuse our test is right tailed Since H1 has > sign

P value = P ( Z > 0.701793268 )

We use excel or Ti - 84 or Ti -83 to calculate the exact p value

Excel :-

Normal distribution is symmetric distribution

P ( Z > a ) = P ( Z < - a )

P ( Z > 0.701793268 ) = P ( Z < - 0.701793268)

Now we find P ( Z < - 0.701793268 ) using excel

Select empty cell ( box ) from excel and type

=NORMSDIST( - 0.701793268 )

Do not forget to type = sign in excel

Press enter

P ( Z < - 0.701793268   ) = 0.241404049

P ( Z > 0.701793268 ) = P ( Z < - 0.701793268)

P ( Z > 0.701793268 ) = 0.241404049

P value = P ( Z > 0.701793268 )

P value = 0.241404049

Ti - 84 and TI - 83 path

Press " Stat "

select " tests "

select " 1 - PropZTest "

po = 0.94    ( Value of p from H0 )

x = 214

n = 225

Prop    > p0 ( Beacuase H1 has > sign )

Select " Calculate "

and press "enter"

z = 0.701793268

p value = 0.241404049

Decision rule

1 ] p value ≤ α then we reject H0

2 ] p value > α then we do not reject H0

p value = 0.241404049   and   α = 0.05.

So Decision is

p value > α then we do not reject H0

Conclusion:-

We do not reject Ho means we are supporting H0 As we are supporting H0 That means we are not supporting H1 and our claim is under H1

Conclusion :-

There is insufficient eveidence to support the claim that " over 94% of patients taking Nex are cured in 8 weeks"

I hope this will help you :)