In 2005, 20% of all U.S. adults said that they had confidence in the U.S. Congress to work in the best interest of the people of the United States. Suppose that in 2015, in a random sample of 145 U.S. adults, 21 reported that they had confidence in the U.S. Congress to work in the best interest of the people of the United States.
Does the sample provide evidence that the proportion of U.S. adults in 2015 who hold this view has decreased since 2005? Test this claim at the 5% significance level.
Let p be the proportion of U.S. adults in 2015 who have confidence in the U.S. Congress.
What are the hypotheses for this test?
Solution :
Given that,
= 0.20
1 - = 0.80
n = 145
x = 21
Level of significance = = 0.05
Point estimate = sample proportion = = x / n = 0.145
This a left (One) tailed test.
The null and alternative hypothesis is,
Ho: p = 0.20
Ha: p < 0.20
Test statistics
z = ( - ) / *(1-) / n
= ( 0.145 - 0.20) / (0.20*0.80) / 145
= -1.661
P-value = P(Z < z )
= P(Z < -1.661 )
= 0.0484
The p-value is p = 0.0484, and since p = 0.0484 < 0.05, it is concluded that the null hypothesis is rejected.
There is sufficient evidence that the proportion of U.S. adults in 2015 who hold this view has decreased since 2005.
In 2005, 20% of all U.S. adults said that they had confidence in the U.S. Congress...
In 2005, 20% of all U.S. adults said that they had confidence in the U.S. Congress to work in the best interest of the people of the United States. Suppose that in 2015, in a random sample of 145 U.S. adults, 21 reported that they had confidence in the U.S. Congress to work in the best interest of the people of the United States. Does the sample provide evidence that the proportion of U.S. adults in 2015 who hold this...
In 2005, 20% of all U.S. adults said that they had confidence in the U.S. Congress to work in the best interest of the people of the United States. Suppose that in 2015, in a random sample of 145 U.S. adults, 21 reported that they had confidence in the U.S. Congress to work in the best interest of the people of the United States Does the sample provide evidence that the proportion of U.S. adults in 2015 who hold this...
In 2005, 20% of all U.S. adults said that they had confidence in the U.S. Congress to work in the best interest of the people of the United States. Suppose that in 2015, in a random sample of 145 U.S. adults, 21 reported that they had confidence in the U.S. Congress to work in the best interest of the people of the United States Does the sample provide evidence that the proportion of U.S. adults in 2015 who hold this...
n 2005, 20% of all U.S. adults said that they had confidence in the U.S. Congress to work in the best interest of the people of the United States. Suppose that in 2015, in a random sample of 145 U.S. adults, 21 reported that they had confidence in the U.S. Congress to work in the best interest of the people of the United States Does the sample provide evidence that the proportion of U.S. adults in 2015 who hold this...
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