Suppose you were told that the 90% confidence interval for the mean μ based on some known σ is (329.87, 356.46). You, however, want a 95% confidence interval. With only the information provided here determine the 95% confidence interval.
I found that the sample mean is 343.165 and the margin of error is 13.295. But how do I figure out the 95% confidence interval without standard deviation?
I found that the sample mean is 343.165 and the margin of error is 13.295. But how do I figure out the 95% confidence interval without standard deviation?
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Role model -
The margin of error is 13.295 as you correctly calculated.
But, the margin of error also equals the sample standard deviation times z* where z* is the z-value for the 90% confidence interval. Looking up in a Standard Normal table, z* = 1.645
That means the sample standard deviation equals 13.295 divided by 1.645 = 8.082.
Now, to find the new 95% confidence interval, look up z* = 1.96
New 95% confidence interval equals sample mean 343.165 +/- (1.96)(8.082)
(327.32, 359.01)
Hope that helped
The margin of error is 13.295 as you correctly calculated.
But, the margin of error also equals the sample standard deviation times z* where z* is the z-value for the 90% confidence interval. Looking up in a Standard Normal table, z* = 1.645
That means the sample standard deviation equals 13.295 divided by 1.645 = 8.082.
Now, to find the new 95% confidence interval, look up z* = 1.96
New 95% confidence interval equals sample mean 343.165 +/- (1.96)(8.082)
(327.32, 359.01)
Hope that helped