Question

assuming that a sample (n = 504) has a sample standard deviation of 2.26, what is the upper bound of a 95% confidence interval if the sample mean is 2.96? 2.96 2.76 3.16 5.94

Explanation:

Step1: Find the critical value

For a 95% confidence interval, the critical value \( z = 1.96\) (from standard normal distribution table).

Step2: Calculate the standard error

The formula for standard error \( SE=\frac{s}{\sqrt{N}}\), where \( s = 2.26\) and \( N = 504\).
\( SE=\frac{2.26}{\sqrt{504}}\approx\frac{2.26}{22.45}\approx0.101\)

Step3: Calculate the upper bound

The formula for the upper bound of a confidence interval is \(\bar{x}+z\times SE\), where \(\bar{x}=2.96\), \( z = 1.96\), and \( SE\approx0.101\)
\( 2.96+1.96\times0.101=2.96 + 0.198\approx3.16\)

Answer:

C. 3.16