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michelle453
21.07.2019 •
Mathematics
Question 21 [t-interval] a random sample of size 18 is drawn from a population that is normally distributed. the sample mean is 58.5, and the sample standard deviation is found to be 11.5. determine a 95% confidence interval about population mean. a. [52.78,64.22] b. [53.78,63.22] c. [53.18,63.81] d. [54.04,62.96]
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Ответ:
Option a. [52.78,64.22]
Step-by-step explanation:
We are given that a random sample of size 18 is drawn from a population that is normally distributed.
Sample mean is 58.5, and the sample standard deviation is found to be 11.5 i.e., X bar = 58.5 and s = 11.5
The pivotal quantity for calculating 95% confidence interval is;
So, 95% confidence interval about population mean is given by;
P(-2.110 <
< 2.110) = 0.95
P(-2.110 <
< 2.110) = 0.95
P(-2.110 *
<
< 2.110 *
) = 0.95
P(X bar - 2.110 *
<
< X bar + 2.110 *
) = 0.95
95% confidence interval about
= [ X bar - 2.110 *
, X bar + 2.110 *
]
= [ 58.5 - 2.110 *
, 58.5 + 2.110 *
]
= [ 52.78 , 64.22 ]
Therefore, 95% confidence interval about population mean is [52.78 , 64.22].
Ответ:
C. 28,524
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