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

UkusakazaL

Answered question

2021-08-01

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 $

Answer & Explanation

beljuA

beljuA

Beginner2021-08-09Added 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 population means confidence interval can be calculated using the formula below:
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 
The values in the confidence interval formula should be substituted.
CI=x±t(α2,df)sn 
=35100±2.473×880028 
=35100±4112.141 
=(30987.859,39212.141) 
(30988,39212) 
Step 5 
Therefore, the 98% confidence interval for the mean account valuation is between $30988 and $39212.

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