What is a

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$98\mathrm{\%}$ confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount.)

$98\mathrm{\%}$ 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$\left(n\right)=28$

Sample mean$\left(\stackrel{\u2015}{x}\right)=\mathrm{\$}35,100}$

Sample standard deviation$\left(s\right)=\mathrm{\$}8,800}$

Step 2

The formula to calculate the confidence interval for population mean is:

$\stackrel{\u2015}{x}\pm {t}_{(\frac{\alpha}{2},df)}\frac{s}{\sqrt{n}}$

Step 3

Here, the population standard deviation is unknown. So, the t-critical value is used.

The degrees of freedom is:$df=n-1=28-1=27$

The critical value for$98\mathrm{\%}$ confidence level at $df=27$ can be found using the t-table. That is,

$t}_{(\frac{\alpha}{2},df)}={t}_{(\frac{0.02}{2},27)$

$=2.473$

Step 4

Substitute the values in the confidence interval formula.

$CI=\stackrel{\u2015}{x}\pm {t}_{(\frac{\alpha}{2},df)}\frac{s}{\sqrt{n}}$

$=35100\pm 2.473\times \frac{8800}{\sqrt{28}}$

$=35100\pm 4112.141$

$=(30987.859,39212.141)$

$\approx (30988,39212)$

Step 5

Thus, the$98\mathrm{\%}$ confidence interval for the mean account valuation is between $30988 and $39212.

The provided information are:

Sample size

Sample mean

Sample standard deviation

Step 2

The formula to calculate the confidence interval for population mean is:

Step 3

Here, the population standard deviation is unknown. So, the t-critical value is used.

The degrees of freedom is:

The critical value for

Step 4

Substitute the values in the confidence interval formula.

Step 5

Thus, the

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