A sample of 50 students is taken from Utah Valley University (UVU).These students spent an average of $175 on books this semester,with a standard deviation of $25.A 95% confidence interval for the average amount of money spent on books for all students at UVU is equal to ________.(Hint: Use Excel function to obtain the critical value. )
A)175 ± 3.47
B)175 ± 7.18
C)175 ± 7.51
D)175 ± 3.86

Question

Quizplus · Accepted Answer

To calculate a 95% confidence interval for the mean, you can use the formula: $\bar{x} \pm (t_{\alpha/2} \times \frac{s}{\sqrt{n}})$, where $\bar{x}$ is the sample mean, $t_{\alpha/2}$ is the critical value from the t-distribution for 95% confidence and 49 degrees of freedom (since n-1 = 50-1 = 49), $s$ is the sample standard deviation, and $n$ is the sample size. Using Excel, the critical value (t_{\alpha/2}) for 49 degrees of freedom at 95% confidence can be found using the T.INV.2T function, which is approximately 2.01. Plugging in the values: $175 \pm (2.01 \times \frac{25}{\sqrt{50}})$, you get $175 \pm 7.18$.

A Sample of 50 Students Is Taken from Utah Valley