Question

In: Statistics and Probability

1. We want to test H0 : p ≥ 0.43 versus Ha : p < 0.43...

1. We want to test H0 : p ≥ 0.43 versus Ha : p < 0.43 . We know that n = 500 and p = 0.3990 .

(a) What is the value of the test statistic? Round your test statistic to 2 digits after the decimal point. (To get an answer good to 2 digits, compute the standard error to 5 digits.)

(b) What is the p-value of the test ? Round your p-value to 3 digits after the decimal point.

(c) Using the p-value method , do we reject or not reject H0 at the .05 level of significance? Reject or Not Reject

Expert Solution

Solution :

Given that,

This is a left tailed test,

a)

Standard error = *(1-) / n = (0.43*0.57) / 500 = 0.02214

Test statistics

z = ( - ) / *(1-) / n

= ( 0.3990 - 0.47) / 0.02214

= -3.21

b)

P-value = P(Z < -3.21 )

= 0.0004.

c)

The p-value is p = 0.0004, and since p = 0.0004 < 0.05, it is concluded that the null hypothesis is rejected.

orchestra answered 2 years ago

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