Chapter PVI, Problem 4RE

(a)

To determine

To give a $95\%$ confidence interval for the average savings in dollars.

Answer to Problem 4RE

The confidence interval is $(49.18,202.83)$ .

Explanation of Solution

It is given in the question that in a full-page as that ran in many U.S. newspaper in August, a Canadian discount pharmacy listed costs of drugs that could be ordered from a web site in Canada. Thus, to find the confidence interval for mean we will use the calculator $\text{TI}-89$ . In the STAT Intsmenu, choose $4:2-$ SampTInt. You must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify the desired level of confidence. Since we have the list for the data as:

U.S.	Canada
131	83
136	72
374	219
370	166
61	17
252	214
263	112
349	50
243	134
166	42
365	200
216	105

And the $\alpha =0.05$ so, by using the calculator $\text{TI}-89$ , the result will be as follows:

  $\begin{array}{l}P=0.0029\\ \text{Margin of error}=76.825\end{array}$

And the confidence interval will be:

  $(49.18,202.83)$

(b)

To determine

To give a $95\%$ confidence interval for the average savings in percent.

Answer to Problem 4RE

  $(40.115,64.218)$ .

Explanation of Solution

It is given in the question that in a full-page as that ran in many U.S. newspaper in August, a Canadian discount pharmacy listed costs of drugs that could be ordered from a web site in Canada. Thus, to find the confidence interval for mean we will use the calculator $\text{TI}-89$ .In the STAT Intsmenu, choose $2:$ TInterval. Specify whether you are using data stored in a list or whether you will enter the mean, standard deviation, and sample size. You must also specify the desired level of confidence.Since we have the list for the data as:

Percentage
37
47
41
55
72
15
57
86
45
75
45
51

And the $\alpha =0.05$ so, by using the calculator $\text{TI}-89$ , the result will be as follows:

The confidence interval will be,

  $(40.115,64.218)$ .

(c)

To determine

To explain which analysis is more appropriate and why.

Answer to Problem 4RE

The average savings in dollars is more appropriate analysis.

Explanation of Solution

It is given in the question that in a full-page as that ran in many U.S. newspaper in August, a Canadian discount pharmacy listed costs of drugs that could be ordered from a web site in Canada. Thus, we can say that the average savings in dollars are more appropriate analysis because it shows the complete value in dollars whereas the average savings in percent is the approximate analysis of the actual savings.

(d)

To determine

To explain how does this comment affect your conclusions above.

Explanation of Solution

It is given in the question that in a full-page as that ran in many U.S. newspaper in August, a Canadian discount pharmacy listed costs of drugs that could be ordered from a web site in Canada. The comment in newspaper says that complete list of all $1500$ drugs available on request. This affect the conclusion that the results are based on the sample taken out form the population and the newspaper is representing that the results are based on the whole sample.