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8.2

8.2

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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8.2
### Statistical Analysis of Cell Phone Ownership A poll of 2,109 randomly selected adults showed that 93% of them own cell phones. The results below are from a test of the claim that 92% of adults own cell phones. The normal distribution is used as an approximation to the binomial distribution, and a 0.01 significance level is assumed for parts (a) through (e). **Test of \( p = 0.92 \) vs \( p \neq 0.92 \):** - **Sample X:** 1960 - **N:** 2109 - **Sample p:** 0.929350 - **95% CI:** (0.914978, 0.943723) - **Z-Value:** 1.58 - **P-Value:** 0.113 #### Analysis **a. Is the test two-tailed, left-tailed, or right-tailed?** - Two-tailed test **b. What is the test statistic?** - The test statistic is 1.58 (rounded to two decimal places). **c. What is the P-value?** - The P-value is 0.113 (rounded to three decimal places). **d. What is the null hypothesis and what do you conclude about it?** - **Identify the null hypothesis:** - \( H_0: p = 0.92 \) - **Conclusion:** - Fail to reject the null hypothesis because the P-value is greater than the significance level, \( \alpha \). In this case, since the P-value of 0.113 is greater than the significance level of 0.01, there is not enough evidence to reject the null hypothesis that 92% of adults own cell phones.
Transcribed Image Text:### Statistical Analysis of Cell Phone Ownership A poll of 2,109 randomly selected adults showed that 93% of them own cell phones. The results below are from a test of the claim that 92% of adults own cell phones. The normal distribution is used as an approximation to the binomial distribution, and a 0.01 significance level is assumed for parts (a) through (e). **Test of \( p = 0.92 \) vs \( p \neq 0.92 \):** - **Sample X:** 1960 - **N:** 2109 - **Sample p:** 0.929350 - **95% CI:** (0.914978, 0.943723) - **Z-Value:** 1.58 - **P-Value:** 0.113 #### Analysis **a. Is the test two-tailed, left-tailed, or right-tailed?** - Two-tailed test **b. What is the test statistic?** - The test statistic is 1.58 (rounded to two decimal places). **c. What is the P-value?** - The P-value is 0.113 (rounded to three decimal places). **d. What is the null hypothesis and what do you conclude about it?** - **Identify the null hypothesis:** - \( H_0: p = 0.92 \) - **Conclusion:** - Fail to reject the null hypothesis because the P-value is greater than the significance level, \( \alpha \). In this case, since the P-value of 0.113 is greater than the significance level of 0.01, there is not enough evidence to reject the null hypothesis that 92% of adults own cell phones.
Expert Solution
Step 1

We have given that 

Sample size n=2109

Favorable cases x=1960

Sample proportion p^=0.929350

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