Question

Construct a confidence interval for the population mean. A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297 29. Find a 99% confidence interval for the true mean checking account balance for local customers. What is the t-Critical Value? What is the Margin of Error (E) rounded to TWO decimal places? What is the Confidence interval? Put in interval form (low, high)

Answer 1

given data are:-

$\bar{x}=664.14,s=297.29,n=14$

df = (n-1) = (14-1) = 13

t critical value for alpha=0.01, df=13 , both tailed test be :-

$t^*=3.012$

the margin of error be:-

$E=\left ( t^**\frac{s}{\sqrt{n}} \right )=\left ( 3.012*\frac{297.29}{\sqrt{14}} \right )\approx \mathbf{239.32}$

the Confidence interval be:-

$=\bar{x}\pm \ margin \ of \ error$

$=664.14\pm 239.32$

$=\mathbf{(424.82,903.46)}$

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