Chapter PVI, Problem 20RE

To determine

To explain is there strong evidence that he will overspend his food allowance.

Answer to Problem 20RE

There in insufficient evident that he will overspend his food allowance.

Explanation of Solution

It is given in the question that a college student is on a "meal program". His budget allows him to spend an average of $\$10$ per day for the semester. Thus, to test the hypothesis for mean we will use the calculator $\text{TI}-89$ . In the STAT Tests menu, choose $2:$ T -Test. You must specify whether you are using data stored in a list or whether you will enter the mean, standard deviation, and size of your sample. You must also specify the hypothesized model mean and whether the test is to be two-tail, lower-tail, or upper-tail. Select whether the test is to be simply computed or whether to display the distribution curve and highlight the area corresponding to the P-value of the test. Since this test is a upper tail test and we have the list as:

Cost ($)
15.2
23.2
3.2
9.8
19.53
6.25
0
8.55
20.05
14.95
23.45
6.75
0
9.01

And we define the hypothesis as:

  $\begin{array}{l}{H}_0:\mu =\$10\\ H_a:\mu >\$10\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}P=0.2600\\ t=0.66\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude thatthere in insufficient evident that he will overspend his food allowance.