Question 1110626
(a) x = 1276 and standard deviation is 39
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(b) 90% confidence interval
alpha(a) = 1 - (90/100) = 0.10
critical probability(p*) = 1 - (a/2) = 0.95
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since the sample size is small(sample size < 30) and the population is normally distributed, we use the student t-tables
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degrees of freedom(df) = 9 - 1 = 8
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from the student t-tables, we see that a df=8 and p*=0.95 has a critical value(t-statistic) of 1.86
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we do not have the population standard deviation, so we use the standard error
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standard error(se) = sample standard deviation/square root(sample size)
se = 39/square root(9) = 13
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margin of error(me) is cv * se
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me = 1.86 * 13 = 24.18 is approximately 24
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90% confidence interval is 1276 + or - 24
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lower limit is 1252
upper limit is 1300
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