1. A class survey in a large class for first-year college students asked, \"Abou
ID: 3220341 • Letter: 1
Question
1. A class survey in a large class for first-year college students asked, "About how many hours do you study in a typical week?". The mean response of the 434 students was xx¯ = 16 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation 8 hours in the population of all first-year students at this university.
What is the 99% confidence interval (±±0.001) for the population mean? Confidence interval is from _____ to _____ hours.
2. (16.25) How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Here are data from students doing a laboratory exercise:
We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 2900 pounds.
Give a 99% confidence interval for the mean load required to pull the wood apart (give your answer with three decimal places).
The sample mean is: _______ (give three decimal places)
99% confidence interval for the mean load is ______ to ______ .
29168 31026 27308 28741 25054 26883 31784 27694 29142 25633 27283 32958 25013 29567 26130 27670 21101 25599 30028 32858 433 38 531 15 066 68 5522 22 1478 7-950 82 290 23 8439 0919 3605 7755 2222 6481 2850 0791 1121 3332 8330 6887 1826 9677 2222Explanation / Answer
(1)
n = 434
x-bar = 16
s = 8
% = 99
Standard Error, SE = /n = 8 /434 = 0.384012289
z- score = 2.575829304
Width of the confidence interval = z * SE = 2.57582930354892 * 0.384012288589855 = 0.989150106
Lower Limit of the confidence interval = x-bar - width = 16 - 0.989150105872632 = 15.01084989
Upper Limit of the confidence interval = x-bar + width = 16 + 0.989150105872632 = 16.98915011
The 99% confidence interval is [15.011 hours, 16.990 hours]
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