Chapter 25, Problem 13E

To determine

To test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company.

Answer to Problem 13E

There is no sufficient evidence to support the claim that drivers might save money by switching to the online company.

Explanation of Solution

It is given from the previous question that:

  $n=10$

The difference table is also given in question as:

Local	Online	PriceDiff
568	391	177
872	602	270
451	488	-37
1229	903	326
605	677	-72
1021	1270	-249
783	703	80
844	789	55
907	1008	-101
712	702	10

Now, the sample mean of the difference will be then,

  $\begin{array}{l}\overline{d}=\frac{177+270-\mathrm{....}+10}{10}\\ =45.9\end{array}$

Now the standard deviation of the difference will be then,

  $\begin{array}{l}{s}_d=\sqrt{\frac{{(177-45.9)}^2+\mathrm{....}+{(10-45.9)}^2}{10-1}}\\ =166.6484\end{array}$

Now, let us define the hypotheses as:

  $\begin{array}{l}{H}_0:{\mu }_d=0\\ H_a:{\mu }_d<0\end{array}$

Thus, the value of test statistics will be as:

  $\begin{array}{l}t=\frac{\overline{d}}{s_d/\sqrt{n}}\\ =\frac{45.9}{166.6484/\sqrt{10}}\\ =0.8710\end{array}$

The degree of freedom will be as:

  $\begin{array}{l}df=n-1\\ =10-1\\ =9\end{array}$

Thus, the P-value will be as:

  $P>0.20$

As we know if the P-value is less than the significance level then reject the null hypothesis. Thus, we have,

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

Thus, we conclude that there is no sufficient evidence to support the claim that drivers might save money by switching to the online company.