Qustion Help * A simple random sample of size n is drawn from a population that
ID: 3318911 • Letter: Q
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Qustion Help * A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, i, is found to be 111, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% oonfidence interval about if the sample size, n, is 20. (b) Construct an 80% cofidenco interval about if the sample size, n, is 12. (c) Construct a 70% confdeno interval abouth1the sample size, n, is 20. (d) Could we have computed the confidence intervals in parts (aHe) if the population had not been normally distributed? Click the ion to view te table of areas under the tdatribution. (a) Construct an 80% onfidenco interval about if the sample size, n, is 20. Lower bound Upper bound: (Use ascending order. Round to one decimal place as needed) (b) Construct an 80% confidence interval about if the sample size, n, is 12. Lower bound:upper bound (Use ascending order. Round to one decimal place as needed.) How does decreasing the sample size affect the margin of error, E?Explanation / Answer
sample mean x = 111
sample standard deviation s = 10
standard error of sample mean = s/ sqrt (n) = 10 / n
(a) 80 % confidence interval = x +- t0.80,dF( 10 / n)
n = 20 ; dF = 19
= 111 +- 1.3277 * (10/20)
= 111 - 2.9689
= (108, 114)
(b)
80 % confidence interval = x +- t0.80,dF( 10 / n)
n = 12 ; dF = 11
= 111 +- 1.3634 * (10/12)
= 111 - 3.9356
= (107.1, 114.9)
decreasing the sample size increasing the confidence interval. The meargin of error also increase (option C is correct)
(c)
70 % confidence interval = x +- t0.80,dF( 10 / n)
n = 20 ; dF = 19
= 111 +- 1.0655 * (10/20)
= 111 - 2.3825
= (108.6, 113.4)
as the percent of confidence interval decreases, the size of interval decreases.
(d) yes, as the population need not to be normally distributed.
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