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.
To Test :-
H0 :- P = 0.20
H1 :- P < 0.20
P = X / n = 21/145 = 0.1448
Test Statistic :-
Z = ( P - P0) / √(P0 * q0 / n)
Z = ( 0.1448 - 0.2 ) / √(( 0.2 * 0.8) /145)
Z = -1.66
Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Z(α) = Z(0.05) = 1.645
Z < -Z(α) = -1.66 < -1.645, hence we reject the null
hypothesis
Conclusion :- We Reject H0
Decision based on P value
P value = P ( Z < -1.66 ) P value = 0.0484
Reject null hypothesis if P value < α = 0.05
Since P value = 0.0484 < 0.05, hence we reject the null
hypothesis
Conclusion :- We Reject H0
There is sufficient evidence to support the claim 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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