Question

Consider the following hypotheses. Ho: p=0.40 Hp#0.40 Given that p=0.26, n = 100, and a =0.10, answer the following questions. a. Determine the p-value for this test. b. What conclusion should be drawn? a. p-value = (Round to three decimal places as needed.) Determine the critical value(s) of the test statistic. b. Choose the correct answer below. O A. Do not reject Ho. There is sufficient evidence that p+0.40. OB. Do not reject Ho There is insufficient evidence that p#0.40. O C. Reject Ho. There is sufficient evidence that p#0.40. OD. Reject Ho. There is insufficient evidence that p#0.40.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p =0.40

H_a : p $\neq$ 0.40

n = 100

$\hat p$ = 0.26

P₀ = 0.40

1 - P₀ = 1 - 0.40 = 0.60

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

=0.26-0.40 / [$\sqrt$(0.40*0.60) / 100]

= -2.86

Test statistic = z =  -2.86

P(z < -2.86) = 0.0021

P-value = 2 * 0.0021 = 0.0042

$\alpha$ = 0.10

P-value < $\alpha$

0.0042 < 0.10

Reject the null hypothesis .

There is sufficient evidence that $\neq$ 0.40

Option D ) is correct.