(b) Suppose that the sample size had been 100 rather than 700 and that 45% of those in the sample indicated that they usually use social media while watching TV. Based on this sample of 100, is there convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV? Use a significance level of 0.05.State the appropriate null and alternative hypotheses.- ○ \( H_0: p = 0.5 \) versus \( H_a: p \neq 0.5 \)- ○ \( H_0: p = 0.5 \) versus \( H_a: p < 0.5 \)- ○ \( H_0: p < 0.5 \) versus \( H_a: p > 0.5 \)- ○ \( H_0: p \neq 0.5 \) versus \( H_a: p = 0.5 \)- ○ \( H_0: p = 0.5 \) versus \( H_a: p > 0.5 \)Find the test statistic and \( p \)-value. (Use a table or technology. Round your test statistic to two decimal places and your \( p \)-value to four decimal places.)\( z = \_\_\_\_\)\( p\text{-value} = \_\_\_\_\)State the conclusion in the problem context.- ○ Fail to reject \( H_0 \). We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.- ○ Fail to reject \( H_0 \). We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.- ○ Reject \( H_0 \). We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.- ○ Reject \( H_0 \). We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.(c) Explain why different conclusions were reached in the hypothesis tests of parts (a) and (b).Getting \_\_\_\_ out of 700 people responding this way as opposed to \_\_\_\_ out of 100 provides much ___ evidence that fewer than half of Americans ages The report "Digital Democracy Survey" describes a large national survey. In a representative sample of Americans ages 14 to 18 years, 45% indicated that they usually use social media while watching TV. Suppose that the sample size was 700.(a) Is there convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV? Use a significance level of 0.05.State the appropriate null and alternative hypotheses.- \( H_0: p = 0.5 \) versus \( H_a: p > 0.5 \)- \( H_0: p \neq 0.5 \) versus \( H_a: p = 0.5 \)- \( H_0: p < 0.5 \) versus \( H_a: p > 0.5 \)- \( H_0: p = 0.5 \) versus \( H_a: p \neq 0.5 \)- \( H_0: p = 0.5 \) versus \( H_a: p < 0.5 \)Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.)\[ z = \_\_\_ \]\[ P\text{-value} = \_\_\_ \]State the conclusion in the problem context.- Fail to reject \( H_0 \). We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.- Fail to reject \( H_0 \). We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.- Reject \( H_0 \). We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.- Reject \( H_0 \). We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.

Given, sample size=700 level of significance=0.05 sample proportion, p=45%=0.45 Since the sample…

The report "Digital Democracy Survey"t describes a large national survey. In a representative sample of Americans ages 14 to 18 years, 45% indicated that they usually use social media while watching TV. Suppose that the sample size was 700. (a) Is there convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV? Use a significance level of 0.05. State the appropriate null and alternative hypotheses. O H,: p = 0.5 versus H,: p > 0.5 Hoip # 0.5 versus H,: p = 0.5 O Ho: p < 0.5 versus H,: p > 0.5 O Ho: p = 0.5 versus H,: p = 0.5 O Ho: P = 0.5 versus H,: p < 0.5 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Fail to reject H,. We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV. Fail to reject H,. We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV. Reject Ho. We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV. Reject H,. We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P