Answer to Question #252467 in Statistics and Probability for SARAH

Question

Average undergraduate cost for tuition, other fees, and boarding for all institutions in the US last year is $19410. A random sample of costs this year for 40 institutions of higher learning indicated that the sample mean was $22098, and the sample standard deviation was $6050. At 0.01 level of significance, is there sufficient evidence to conclude that the cost has increased

Answer 1

Solution:

We are given a sample standard deviation but since the sample size is greater than 30, we can use the z distribution instead of the t distribution.

$\begin{aligned} &H_{0}: \mu=19410 \\ &H_{1}: \mu>19410 \end{aligned}$  

Test Statistic: $z=\dfrac{\bar{x}-\mu}{\sigma / \sqrt{n}}$

Rejection Region: $\left\{z: z \geq z_{\alpha}=z_{0.01}=2.33\right\}$

 $z=\dfrac{22098-19410}{6050 / \sqrt{40}}=2.81$  

Reject H₀ since the value of the test statistic 2.81, is greater than the critical value 2.33.

Thus, there is sufficient evidence to conclude that the cost of attendance has increased