As part of an annual review of its accounts, a discount brokerage selects a random sample of 28 customers. Their accounts are reviewed for total account valuation, which showed a mean of $35,100, with a sample standard deviation of $8,800. What is a 98\% confidence interval for the mean account valuation of the population of customers?

UkusakazaL 2021-08-01 Answered
As part of an annual review of its accounts, a discount brokerage selects a random sample of 28 customers. Their accounts are reviewed for total account valuation, which showed a mean of $35,100, with a sample standard deviation of $8,800. (Use t Distribution Table.)
What is a 98% confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount.)
98% confidence interval for the mean account valuation is between $ and $
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beljuA
Answered 2021-08-09 Author has 2 answers
Step 1
The provided information are:
Sample size (n)=28
Sample mean (x)=$35,100
Sample standard deviation (s)=$8,800
Step 2
The formula to calculate the confidence interval for population mean is:
x±t(α2,df)sn
Step 3
Here, the population standard deviation is unknown. So, the t-critical value is used.
The degrees of freedom is: df=n1=281=27
The critical value for 98% confidence level at df=27 can be found using the t-table. That is,
t(α2,df)=t(0.022,27)
=2.473
Step 4
Substitute the values in the confidence interval formula.
CI=x±t(α2,df)sn
=35100±2.473×880028
=35100±4112.141
=(30987.859,39212.141)
(30988,39212)
Step 5
Thus, the 98% confidence interval for the mean account valuation is between $30988 and $39212.
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