What do you make of Mitt? Twenty-nine college students, identified as having a p
ID: 3153591 • Letter: W
Question
What do you make of Mitt? Twenty-nine college students, identified as having a positive attitude about Mitt Romney as compared to Barack Obama in the 2012 presidential election, were asked to rate how trustworthy the face of Mitt Romney appeared, as represented in their mental image of Mitt Romney’s face. Ratings were on a scale of 0 to 7, with 0 being “not at all trustworthy” and 7 being “extremely trustworthy.” Here are the 29 ratings:20
(a)Suppose we can consider this an SRS of all U.S. college students. Make a stemplot. Is there any sign of major deviation from Normality?
(b)Give a 95% confidence interval for the mean rating
(c)Is there significant evidence at the 5% level that the mean rating is greater than 3.5 (a neutral rating)?
Explanation / Answer
a)
Consider:
Looking at this plot, there are no major deviations from normality.
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b)
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 3.937931034
t(alpha/2) = critical t for the confidence interval = 2.048407142
s = sample standard deviation = 0.801522566
n = sample size = 29
df = n - 1 = 28
Thus,
Lower bound = 3.633048156
Upper bound = 4.242813913
Thus, the confidence interval is
( 3.633048156 , 4.242813913 ) [ANSWER]
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c)
As this whole interval in b) is totally greater than 3.5, then YES, there is significant evidence at the 5% level that the mean rating is greater than 3.5. [CONCLUSION]
Stem Leaves 2 6 6 8 3 0 2 2 3 3 4 6 7 7 8 9 9 9 9 4 1 1 2 2 6 6 7 9 5 0 0 3 7Related Questions
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