In a random sample of 1066 U.S. adults, 580 think that the U.S. government is doing too little to protect the environment. In another random sample of 1038 U.S. adults taken 10 years ago, 514 think that the U.S. government is doing too little to protect the environment. At α = 0.10, can you reject the claim that the proportion of U.S. adults who think that the U.S. government is doing too little to protect the environment has not changed?Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.Find the critical value(s) and identify the rejection region(s).Find the appropriate standardized test statistic. If convenient, use technology.Decide whether to reject or fail to reject the null hypothesis.Interpret the decision in the context of the original claim.

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Description: In a random sample of 1066 U.S. adults, 580 think that the U.S. government is doing too little to protect the environment. In another random sample of 1038 U.S. adults taken 10 years ago, 514 think that the U.S. government is doing too little to prot

Given Information: Sample size (n1) = 1066 Out of which x1 = 580 think that the U.S. government is doing too little to protect the environment. Sample size (n2) = 1038 Out of which x2 = 514 Significance level α=0.10 1) State the hypothesis as follows: Null Hypothesis H0:p1=p2 i.e., proportion of U.S. adults who think that the U.S. government is doing too little to protect the environment has not changed. Alternative Hypothesis Ha:p1≠p2 i.e., proportion of U.S. adults who think that the U.S. government is doing too little to protect the environment has changed. 2) Since, the alternative hypothesis includes "not equal to" operator, this is a two tailed test. 3) Using a standard normal table, critical values for a two tailed test at 0.10 significance level are: -1.645 and +1.645 If computed value of the test statistic is less than -1.645, it falls in the rejection region and so we reject H0. If computed value of the test statistic is greater than +1.645, it falls in the rejection region and we reject H0. 4) Test statistic is given by the formula: z=p^1-p^2p^1-p^1n1+1n2 Sample proportion of sample 1 is obtained as follows; p^1=x1n1=5801066=0.5440900563 Sample proportion of sample 2 is obtained as follows; p^2=x2n2=5141038=0.4951830443 p^=x1+x2n1+n2=580+5141066+1038=10942104=0.5199619772≈0.519962 Substitute the values in the formula of the test statistic: z=p^1-p^2p^1-p^1n1+1n2=0.5440900563-0.49518304430.5199621-0.51996211066+11038=0.0489070120.24960151860.001901477441=0.0489070120.02178558369≈2.245 Thus, the value of the test statistic is 2.245 Since, computed value of the test statistic is greater than the critical value 1.645, we reject the null hypothesis. There is sufficient evidence to reject the claim that the proportion of U.S. adults who think that the U.S. government is doing too little to protect the environment has not changed.

Answered: In a random sample of 1066 U.S. adults,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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In a random sample of 1066 U.S. adults, 580 think that the U.S. government is doing too little to protect the environment. In another random sample of 1038 U.S. adults taken 10 years ago, 514 think that the U.S. government is doing too little to protect the environment. At α = 0.10, can you reject the claim that the proportion of U.S. adults who think that the U.S. government is doing too little to protect the environment has not changed?

Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.
Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
Find the critical value(s) and identify the rejection region(s).
Find the appropriate standardized test statistic. If convenient, use technology.
Decide whether to reject or fail to reject the null hypothesis.
Interpret the decision in the context of the original claim.

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