Question

A poll of 2,084 randomly selected adults showed that 94% of them own cell phones. The technology display below ret from a test of the claim that 92% of adults own cell phones. Use the normal distribution as an approximation to the bin distribution, and assume a 0.01 significance level to complete parts (a) through (e). Test of p = 0.92 vs p+0.92 Z-Value P-value Sample p 95% CI N Sample X 0.000 4.01 (0.930869,0.956847) 1 1967 2,084 0.943858 a. Is the test two-tailed, left-tailed, or right-tailed? O Right tailed test O Two-tailed test Left-tailed test b. What is the test statistic? The test statistic is (Round to two decimal places as needed.) c. What is the P-value? The P-value is (Round to three decimal places as needed.) d. What is the null hypothesis and what do you conclude about it? Idently the null hypothesis OA HD > 092 O B. Hy p0.92 OC. HỌ p< 0 92 OD. H, p=0.92 Choose the correct answer below ON Reject the null hypothesis because the P-value is less than or equal to the significance level, OB. Fall to reject the null hypothesis because the P value is greater than the significance level, a OC Reject the will hypothesis because the value is greater than the significance level, a Click to select your answer(s)

Answer 1

(1)

(a) This is a two tailed test (Since the alternative contains the $\neq$ sign)

(b) The test statistic is Z = 4.01

(c) The p value is 0.000

(d) The null hypothesis is Option D: H0: p = 0.92

Option A: Reject the null hypothesis because the p value is less than or equal to the significance level $\alpha$.

___________________________________________________________________

(2) The Hypothesis: Option B

H0: p = 0.20

H1: p < 0.20

The Test Statistic:

$\hat{p}$ = 1290 / 6990 = 0.1845

Z=P P 0.1845 -0.2 -= -3.24 0.20.8 V 6990

The p value is 0.001

Since the p value is less than the significance level, reject the null hypothesis. There is sufficient evidence to support the claim that the return rate is less than 20%.

_____________________________________________________________