A random sample of the closing stock prices in dollars for a company in a recent
ID: 3053175 • Letter: A
Question
A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that ? is $1.77Construct the 90?%
and 99?% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.
16.53
20.47
20.58
18.19
19.25
20.97
20.42
15.61
17.92
15.55
18.47
17.98
21.02
20.25
18.45
20.98
The? 90% confidence interval is
The? 99% confidence interval is
Which statement below interprets the results? correctly?
The probability that the mean closing stock price is in the? 90% confidence interval is about? 90% and the probability that the mean closing stock price is in the? 99% confidence interval is about? 99%.
?90% of the mean closing stock prices are in the? 90% confidence interval and? 99% of the mean closing stock prices are in the? 99% confidence interval.
The? 90% confidence interval contains the mean closing stock price? 90% of the time and the? 99% confidence interval contains the mean closing stock price? 99% of the time.
There is? 90% confidence that the mean closing stock price is in the? 90% confidence interval and? 99% confidence that the mean closing stock price is in the? 99% confidence interval.
Explanation / Answer
CI for = 90%
n = 16
mean = 18.915
t-value of 90% CI = 1.7531
std. dev. = 1.77
SE = std.dev./sqrt(n) = 0.44250
ME = t*SE = 0.77572
Lower Limit = Mean - ME = 18.13928
Upper Limit = Mean + ME = 19.69072
The 90% CI is (18.1393 , 19.6907 )
CI for = 99%
n = 16
mean = 18.915
t-value of 99% CI = 2.9467
std. dev. = 1.77
SE = std.dev./sqrt(n) = 0.44250
ME = t*SE = 1.30392
Lower Limit = Mean - ME = 17.61108
Upper Limit = Mean + ME = 20.21892
The 99% CI is (17.6111 , 20.2189 )
There is? 90% confidence that the mean closing stock price is in the? 90% confidence interval and? 99% confidence that the mean closing stock price is in the? 99% confidence interval.
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