### Hypothesis Testing for Proportion**Problem Statement:**A simple random sample of size $ n = 200 $ drivers with a valid driver's license is asked if they drive an American-made automobile. Of the 200 drivers surveyed, 123 responded that they drive an American-made automobile. Determine if a majority of those with a valid driver's license drive an American-made automobile at the $ \alpha = 0.05 $ level of significance.**Calculate the test statistic.**- **Test Statistic =** [ ] $*Round to two decimal places as needed.*)#### Instructions:1. **Hypotheses:** - Null Hypothesis (\(H_0$): $ p = 0.5 $ - Alternate Hypothesis ($H_1$): $ p > 0.5 $2. **Level of Significance:** - $ \alpha = 0.05 $3. **Sample Data:** - Sample size ($ n $) = 200 - Number of successes ($ X $) = 1234. **Sample Proportion:** - $ \hat{p} = \frac{X}{n} = \frac{123}{200} = 0.615 $5. **Test Statistic Calculation:** - Use the formula for the test statistic for population proportion: \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]#### Available Options:- **Help me solve this** (interactive tutorial assistance)- **View an example** (see a similar example solved step-by-step)- **Get more help** (access further resources)- **Clear all** (reset the problem)- **Check answer** (submit for correctness check)#### Statistical Tool Note:Make sure to use the statistical tool or calculator to input the proportions and check against the critical value at $ \alpha = 0.05 $ for the given hypothesis.---#### Practical Implication:Understanding the concept of hypothesis testing allows you to make informed decisions based on statistical evidence. In this case, the test will help determine if more than half of the surveyed drivers prefer American-made cars, given the responses from the sample.

Number of successes is x= 123. Sample size is n =200. Level of significance is…

Answered: A simple random sample of size n=200…

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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The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 346 seconds. For a sample of 58 patients, the mean time in which the medicine relieved pain was 352 seconds. Assume the population standard deviation is 23. Find the P-value of the test statistic. 囲 Tables E Keypad Keyboard Shortcuts 0.0582 %3D IX
Random samples of students at 107 four-year colleges were interviewed several times since 1998. Of the students who reported drinking alcohol, the percentage who reported bingeing at least three times within the past two weeks was 41.1% of 336 students in 1998 and 21.6% of 843 students in 2004. a. Estimate the difference between the proportions in 2004 and 1998, and interpret. b. Find the standard error for this difference. Interpret it. c. Define the two relevant population parameters to compare in the context of this exercise. d. Construct and interpret a 90% confidence interval to estimate the true difference. e. State the assumptions for the confidence interval in part d to be valid. ... A. The number of students in the population in 2004 who reported drinking alcohol that binged at least three times within the past two weeks. B. The proportion of the student population in 1998 who reported drinking alcohol that binged at least three times within the past two weeks. C. The number…
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a survey is conducted to compare the proportions of men and women whoaccess their bank statements online. Denoting the population propotions by Pm and Pw, a two-proportion z-test is carried out to test Ho: pm = pw against Ha: pm > pw. The values of the test statistic is found to be z = 0.784, and the p-value for the test is found to be 0.216. Which of the following is the correct interpretation of the p-value? a) given that ha is true, the probability of getting a value of z at least as large as 0.784 is 0.216. b) given the results of the survey, the probability that Pm > Pw is 0.216. c) given the results of the survey, the probability that Pm = Pw is 0.216. d) none of the above

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