Question

A random sample of n = 1,300 observations from a binomial population produced x = 618.

(a) If your research hypothesis is that p differs from 0.5, what hypotheses should you test?

H₀: p ≠ 0.5 versus H_a: p = 0.5 H₀: p < 0.5 versus H_a: p > 0.5     H₀: p = 0.5 versus H_a: p > 0.5 H₀: p = 0.5 versus H_a: p < 0.5 H₀: p = 0.5 versus H_a: p ≠ 0.5

(b) Calculate the test statistic and its p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

z	=
p-value	=

Use the p-value to evaluate the statistical significance of the results at the 1% level.

H₀ is not rejected since the p-value is not less than 0.01. H₀ is rejected since the p-value is not less than 0.01.     H₀ is not rejected since the p-value is less than 0.01. H₀ is rejected since the p-value is less than 0.01.

(c) Do the data provide sufficient evidence to indicate that p is different from 0.5?

Yes, the data provide sufficient evidence to indicate that p is different from 0.5. No, the data do not provide sufficient evidence to indicate that p is different from 0.5.    

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

n =1300

x = 618

Point estimate = sample proportion = = x / n = 0.475

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.5

Ha: p 0.5

Test statistics

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

= ( 0.475 - 0.5) / (0.5*0.5) / 1300

= -1.775

P-value = 2 * P(Z < z )

= 2 * P(Z < -1.775 )

= 2 * 0.0379

= 0.9621

Since , P-value > 0.01, fail to reject .

No, the data do not provide sufficient evidence to indicate that p is different from 0.5.