Question

A watchdog association claims that the percentage of Americans who agree that the government is inefficient and wasteful is different from 70%. A researcher wants to test this claim. The researcher conducts a survey and finds that out of a random sample of 1175 Americans, 785 agreed with this view.

17. The standardized test statistic for a hypothesis test which tests whether the sample proportion is equal to the hypothesized population proportion is equal to: a, 2.387 b 2.378 c. -2.387

18. The probability value of the event that the standardized test statistic would assume a value as large as that calculated in question 17 is: a. 0.0017 b. 0.017 c. 0.17

19. By comparing the probability value calculated in question 16 with a level of significance of 0.01 in a hypothesis test, we can conclude that a. the proportion of Americans who agree that the government is inefficient and wasteful is not equal to 70%. b. the proportion of Americans who agree that the government is inefficient and wasteful is equal to 70% c. the proportion of Americans who agree that the government is inefficient and wasteful is greater than 70%

20. The 99% confidence interval for the proportion of Americans who agree that the government is inefficient and wasteful will fall between: a. (0.632, 0.703) b. (0.641, 0/695) c. (0.645, 0.691)

Answer 1

Answer:

17) c. -2.387

18) b. 0.017

19) b. the proportion of Americans who agree that the government is inefficient and wasteful is equal to 70%

20) a. (0.632, 0.703)

Solution is given below:

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We have given
P0=0.70
n=1175
x=785
P=785/1175 =0.668085
significance level of 0.01.

(a) What are the null and alternative hypotheses?
H0: P=P0
Ha: P not eual to P0

(b) What is the test statistic?
z=(P-P0)/sqrt(P0*(1-P0)/n)

=(0.668085-0.70)/sqrt(0.70*(1-0.7)/1175)

=-2.3872

The standardized test statistic for a hypothesis test = c. -2.387

18. The probability value of the event that the standardized test statistic would assume a value as large as that calculated in question 17 is:

Answer: b. 0.017

probability value of the event that the standardized test statistic would assume a value as large astest statistics

=2*p(Z<-2.387)

=2*0.0084

=0.017

19. By comparing the probability value calculated in question 16 with a level of significance of 0.01 in a hypothesis test, we can conclude that

Answer :

b. the proportion of Americans who agree that the government is inefficient and wasteful is equal to 70%

because p-value > 0.01 hence we do not reject H0 hence conclude that the proportion of Americans who agree that the government is inefficient and wasteful is equal to 70%

20. The 99% confidence interval for the proportion of Americans who agree that the government is inefficient and wasteful

Answer a. (0.632, 0.703)

CI =P0 +/- z*sqrt(P0*(1-P0)/n)

z=2.57583

CI=(0.668085-2.57583*sqrt(0.70*(1-0.7)/1175) ,  0.668085+2.57583*sqrt(0.70*(1-0.7)/1175))

CI=(0.633649495 ,0.702520717)

The 99% confidence interval for the proportion of Americans who agree that the government is inefficient and wasteful will fall between: Answer a. (0.632, 0.703)