Question

a random sample of 22 college mens basketball games during the last season had an average attendance of 5,132 with a sample standard deviation of 1,756. complete parts a and b below.
a. construct a 90% confidence interval to estimate the average attendance of a college mens basketball game during the last season.
the 90% confidence interval to estimate the average attendance of a college mens basketball game during the last season is from a lower limit of to an upper limit of .
(round to the nearest whole numbers.)

Explanation:

Step1: Determine degrees of freedom and t - value

The sample size $n = 22$, so the degrees of freedom $df=n - 1=22-1 = 21$. For a 90% confidence interval, the significance level $\alpha=1 - 0.90 = 0.10$, and $\frac{\alpha}{2}=0.05$. Looking up in the t - distribution table, $t_{\frac{\alpha}{2},df}=t_{0.05,21}=1.721$.

Step2: Calculate the margin of error

The formula for the margin of error $E=t_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}}$, where $s = 1756$ is the sample standard deviation and $n = 22$. So $E = 1.721\times\frac{1756}{\sqrt{22}}\approx1.721\times\frac{1756}{4.6904}\approx1.721\times374.4\approx644$.

Step3: Calculate the confidence interval

The sample mean $\bar{x}=5132$. The lower limit of the confidence interval is $\bar{x}-E=5132 - 644=4488$. The upper limit is $\bar{x}+E=5132 + 644=5776$.

Answer:

The lower limit is 4488 and the upper limit is 5776.