Part a)
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
Critical value t(α/2, n-1) = t(0.1 /2, 22- 1 ) =
1.721 ( from t table )
106 ± t(0.1/2, 22 -1) * 10/√(22)
Lower Limit = 106 - t(0.1/2, 22 -1) 10/√(22)
Lower Limit = 102.3308
Upper Limit = 106 + t(0.1/2, 22 -1) 10/√(22)
Upper Limit = 109.6692
90% Confidence interval is ( 102.3308 , 109.6692 )
Part b)
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
Critical value t(α/2, n-1) = t(0.1 /2, 27-
1 ) = 1.706 ( from t table )
106 ± t(0.1/2, 27 -1) * 10/√(27)
Lower Limit = 106 - t(0.1/2, 27 -1) 10/√(27)
Lower Limit = 102.7168
Upper Limit = 106 + t(0.1/2, 27 -1) 10/√(27)
Upper Limit = 109.2832
90% Confidence interval is ( 102.7168 , 109.2832 )
Part b)
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
Critical value t(α/2, n-1) = t(0.01 /2,
22- 1 ) = 2.831 ( from t table )
106 ± t(0.01/2, 22 -1) * 10/√(22)
Lower Limit = 106 - t(0.01/2, 22 -1) 10/√(22)
Lower Limit = 99.9643
Upper Limit = 106 + t(0.01/2, 22 -1) 10/√(22)
Upper Limit = 112.0357
99% Confidence interval is ( 99.9643 , 112.0357 )
Part d)
No, we cannot calculate the confidence interval if population is not normally distributed.
A simple random sample of size n is drawn from a population that is normally distributed....
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10 (a) Construct a 98% confidence interval about if the sample size, n, s 14 (b) Construct a 98% confidence interval about μ if the sample size, n, is 19 (c) Construct a 99% confidence interval about if the sample size, n, s 14 (d)...
A simple random sample of size nis drawn from a population that is normally distributed the sample mean is found to be 113, and the sample standard deviations, is found to be 10 (a) Construct a 95% confidence interval about if the sample size is 22 (b) Construct a 95% confidence interval about the sample on 26 (c) Construct a 90% confidence interval about the sample size is 22 (d) Could we have computed the confidence intervals in parts(a-c) if...
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̅, is found to be 107 , and the sample standard deviation, s, is found to be 10 .(a) Construct a 98 % confidence interval about μ if the sample size, n, is 22 .(b) Construct a 98 % confidence interval about μ if the sample size, n, is 12 .(c) Construct a 95 % confidence interval about μ if the...
simple random sample of size n is drawn from a population that is normally distributed. The sample mean, X. is found to be 111, and the sample standard deviation is found to be 10. a) Construct a 95% confidence interval about if the sample size, n, is 28. b) Construct a 95% confidence interval about if the sample size, n, is 11 c) Construct a 90% confidence interval about if the sample size, n, is 28 ) Could we have...
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̅, is found to be 109 , and the sample standard deviation, 5 , is found to be 12 .(a) Construct a 96 % confidence interval about μ if the sample size, n, is 23 .(b) Construct a 96 % confidence interval about μ if the sample size, n, is 16 .(c) Construct a 90 % confidence interval about μ if...
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, X, is found to be 110, and the sample standard deviation, s, is found to be 10 (a) Construct an 80% confidence interval about p if the sample size, n, is 14 (b) Construct an 80% confidence interval about if the sample size, n, is 18. (c) Construct a 98% confidence interval about if the sample size, n, is 14. (d)...
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar x, is found to be 107, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about mu μ if the sample size, n, is 18. (b) Construct a 98% confidence interval about mu μnif the sample size, n, is 12. c) Construct a 96% confidence interval about mu μ if...
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar x, is found to be 108, and the sample standard deviation, s, is found to be 10. (a) Construct a 95% confidence interval about mu μ if the sample size, n, is 12. (b) Construct a 95% confidence interval about mu μ if the sample size, n, is 23. (c) Construct a a 96 96% confidence...