Question

A random sample of n = 1,400 observations from a binomial population produced x = 252.

(a) If your research hypothesis is that p differs from 0.2, what hypotheses should you test?

H₀: p = 0.2 versus H_a: p > 0.2

H₀: p = 0.2 versus H_a: p ≠ 0.2   

H₀: p = 0.2 versus H_a: p < 0.2

H₀: p < 0.2 versus H_a: p > 0.2

H₀: p ≠ 0.2 versus H_a: p = 0.2

(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 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.

(c) Do the data provide sufficient evidence to indicate that p is different from 0.2?

Yes, the data provide sufficient evidence to indicate that p is different from 0.2.

No, the data do not provide sufficient evidence to indicate that p is different from 0.2.    

You may need to use the appropriate appendix table or technology to answer this question.

Answer 1

The statistic software output for this problem is:

H₀ : p = 0.2
H_A : p ≠ 0.2

z = -1.87

P-value = 0.0614

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

No, the data do not provide sufficient evidence to indicate that p is different from 0.2