In 2007, 50% of Americans said they did not trust the media. In a 2017 poll of 5
ID: 3229441 • Letter: I
Question
In 2007, 50% of Americans said they did not trust the media. In a 2017 poll of 572 adults nationwide, 248 stated they did not trust the media. At the alpha equals 0.10 level of significance, is there evidence to support the claim that the percentage of Americans that do not trust the media to report fully and accurately has decreased since 2007?
Which of the following is the best to describe the test?
A. One sample proportion, left-tailed, t-test
B. One sample proportion, right-tailed, z-test
C. One sample mean, left-tailed, z-test
D. One sample proportion, left-tailed, z-test
E. One sample mean, right-tailed, t-test
What will be the test hypotheses?
A. H0: p=0.5 vs H1: p<0.5
B. H0: p=0.5 vs H1: p>0.5
C. H0: p=0.5 vs H1: p0.5
D. H0: µ(M-P)0 vs H1: µ(M-P)=0
E. H0: µ(M-P)0 vs H1: µ(M-P)=0
What is the critical value in the test?
A. -1.5379
B. -1.2816
C. -1.7942
D. -2.0505
E. -0.7689
What is the test statistic in the test?
A. -3.1677
B. -3.1777
C. -3.0677
D. -3.2877
E. -2.9677
What should we do about the hypotheses?
A. Do not reject the alternative hypothesis.
B. Accept both hypotheses.
C. Reject the null hypothesis.
D. Accept the null hypothesis.
E. Reject both hypotheses.
What is the research conclusion?
A. There is sufficient evidence to conclude that the average of Americans that do not trust the media was not 50%.
B. There is sufficient evidence to conclude that the percentage of Americans that do not trust the media was decreaded.
C. There is insufficient evidence to conclude that the average percentage of Americans that do not trust the media was 50%.
D. There is sufficient evidence to conclude that the average age of a mother at the time of her first childbirth was not 50%.
E. There is sufficient evidence to conclude that the percentage of Americans that do not trust the media was not decreased.
Compute the upper boundary of the 97% C.I. for the estimated population proportion.
A. 0.4789
B. 0.4589
C. 0.5989
D. 0.3589
Explanation / Answer
C. One sample mean, left-tailed, z-test as we need to check the claim of decrease and also np>5
Test hypothesis will be
A. H0: p=0.5 vs H1: p<0.5
For alpha =0.10
Critical value is
B. -1.2816
Test statistics is
z=(phat-p)/SEp
Where SEp=sqrt(pq/n)=0.02 & phat=0.43
Hence z=(0.43-0.5)/0.02=-3.1777 i.e B
As z critical > a statistics we reject the null hypothesis
C. Reject the null hypothesis.
As per alternative hypothesis
answer is
B. There is sufficient evidence to conclude that the percentage of Americans that do not trust the media was decreaded.
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