Question

A random sample of n = 1,400 observations from a binomial population produced x = 527 successes. You wish to show that p differs from 0.4. Calculate the appropriate test statistic. (Round your answer to two decimal places.)

z =

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

Do the conclusions based on a fixed rejection region of |z| > 1.96 agree with those found using the p-value approach at α = 0.05?

A.Yes, both approaches produce the same conclusion.

B.No, the p-value approach rejects the null hypothesis when the fixed rejection region approach fails to reject the null hypothesis.

C. No, the fixed rejection region approach rejects the null hypothesis when the p-value approach fails to reject the null hypothesis.

Should they?

Yes

No

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.40

Ha : p 0.40

n = 1400

x =57

= x / n = 527/ 1400 =0.38

P0 = 0.40

1 - P0 = 1 - 0.40 =0.60

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.38-0.40/ [(0.40*0.60) / 1400]

= -1.80

Test statistic = z = -1.80

P-value =P(|z|>1.8)

=2*P(Z>1.8)

=2*0.035

=0.0718

P-value=0.0718

|Z|<1.96 hence we fail to reject Ho

Do the conclusions based on a fixed rejection region of |z| > 1.96 agree with those found using the p-value approach at α = 0.05?

A.Yes, both approaches produce the same conclusion.

Option A is correct

C. No, the fixed rejection region approach rejects the null hypothesis when the p-value approach fails to reject the null hypothesis.

Ans;No