Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
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Chapter 25, Problem 15E
To determine
To write a 90% confidence interval for the
Expert Solution & Answer
Answer to Problem 15E
We are 90% confident that the mean difference in temperature between summer and winter in Europe is between (−41.3251,−32.3415)0F .
Explanation of Solution
Now, the table of the mean high temperatures is given in the question. So, let us find the difference between the means of summer and winter as:
Now let us check the conditions for inference as:
Random condition: It is not satisfied but we assume that the measurements of wind speeds are representative for the population.
Independent condition: It is not satisfied because if the wind speed 6 hours from now is very fast then the wind speed at this moment will very likely also be fast.
Normal condition: It is satisfied because the histogram of the differences symmetric and uni-model.
Thus, all the conditions are not met.
Now, it is also given that:
n=12c=90%
The sample mean difference is calculated as:
ˉd=−41−36−....−55−4712=−36.8333
And the sample standard deviation of the difference is as:
sd=√(−41−(−36.8333))2+(−36−(−36.8333))2+....+(−55−(−36.8333))2+(−47−(−36.8333))212−1=8.6638
The degree of freedom is as:
df=n−1=12−1=11
And therefore the t -value will be as:
t=1.796
Thus, the confidence interval is then be as:
ˉd−tα/2×sd√n=−36.8333−1.796×8.6638√12=−41.3251ˉd+tα/2×sd√n=−36.8333+1.796×8.6638√12=−32.3415
Thus, we conclude that we are 90% confident that the mean difference in temperature between summer and winter in Europe is between (−41.3251,−32.3415)0F .
Chapter 25 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Ch. 25 - Prob. 1ECh. 25 - Prob. 2ECh. 25 - Prob. 3ECh. 25 - Prob. 4ECh. 25 - Prob. 5ECh. 25 - Prob. 6ECh. 25 - Prob. 7ECh. 25 - Prob. 8ECh. 25 - Prob. 9ECh. 25 - Prob. 10E
Ch. 25 - Prob. 11ECh. 25 - Prob. 12ECh. 25 - Prob. 13ECh. 25 - Prob. 14ECh. 25 - Prob. 15ECh. 25 - Prob. 16ECh. 25 - Prob. 17ECh. 25 - Prob. 18ECh. 25 - Prob. 19ECh. 25 - Prob. 20ECh. 25 - Prob. 21ECh. 25 - Prob. 22ECh. 25 - Prob. 23ECh. 25 - Prob. 24ECh. 25 - Prob. 25ECh. 25 - Prob. 26ECh. 25 - Prob. 27ECh. 25 - Prob. 28E
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