Question

You wish to test the following claim at a significance level of α=0.10α=0.10.

You wish to test the following claim at a significance level of a = 0.10 Ho:p = 0.82 H1:2 +0.82 You obtain a sample of size 588 in which there are 492 successful observations. What is the test statistic for this sample? (Report answer accurate to 3 decimal places.) What is the p-value for this sample? (Report answer accurate to 4 decim al places.) Questions ► Q 1 (0/1) Q2 (0/1) Q3 (0/3) Q4 (0/3) Q5 (0/5) Q6 (0/5) Q7 (0/2) ► Q8 (0/1) Q 9 (0/2) Q 10 (0/1) Q 11 (0/4) Q 12 (0/4) Q 13 (0/4) Q 14 (0/4) Q 15 (0/4) Q 16 (0/4) Q 17 (0/4) Q 18 (0/4) ► Q 19 (0/6) ► Q 20 (0/4) Q21 (0/2) The p-value is less than or equal to) a greater than a This test statistic leads to a decision to Oreject the null accept the null O fail to reject the null Grade: 0/68 Print Version As such, the final conclusion is that Othere is sufficient evidence to conclude that the population proportion is not equal to 0.82. Othere is not sufficient evidence to conclude that the population proportion is not equal to 0.82. Othere is sufficient evidence to conclude that the population proportion is equal to 0.82. Othere is not sufficient evidence to conclude that the population proportion is equal to 0.82.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.82

H_a : p $\neq$ 0.82

$\hat p$ = x / n = 492 / 588 = 0.8367

Test statistic = z

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

= 0.8367 - 0.82 / [$\sqrt$(0.82 * 0.18) / 588]

= 1.056

P-value = 0.2909

$\alpha$ = 0.10

The P-value is greater than  $\alpha$

Fail to reject the null hypothesis .

there is not sufficient evidence to conclude that the population proportion is espalto 0 82