Chapter PVI, Problem 19RE

(a)

To determine

To examine the differences in the percentages for each country and find out which of these countries seem to be outliers and what do they have in common.

Answer to Problem 19RE

The outliers are countries Spain, Italy and Portugal.

Explanation of Solution

It is given in the question that the researchers want to find out who reads the newspaper more, men or women. Thus, let us calculate the differences in the percentages for each country and construct a graph to examine as:

Country	Men	Women	Difference
Belgium	56.3	45.5	10.8
Denmark	76.8	70.3	6.5
Germany	79.9	76.8	3.1
Greece	22.5	17.2	5.3
Spain	46.2	24.8	21.4
Ireland	58	54	4
Italy	50.2	29.8	20.4
Luxembourg	71	67	4
Netherlands	71.3	63	8.3
Austria	78.2	74.1	4.1
Portugal	58.3	24.1	34.2
Finland	93	90	3
Sweden	89	88	1
UK	32.6	30.4	2.2

So, the graph for the difference is as follows:

  

Thus, by looking at the dot plot for the differences in the percentages for each country between men and women we can see that there are three outliers on the right hand side and if we exclude those outliers than the rest of the points form nearly a normally distributed graph. Thus, the outliers are countries Spain, Italy and Portugal. And the countries in the outliers have in common that they are all Mediterranean countries.

(b)

To determine

To explain is there evidence that in Europe men are more likely than women to read the newspaper, after eliminating the outlier.

Answer to Problem 19RE

European men are more likely than women to read newspaper.

Explanation of Solution

It is given in the question that the researchers want to find out who reads the newspaper more, men or women.Thus, to find out is there any difference we will use the calculator $\text{TI}-89$ . Thus, if the data are stored in two lists, say, $\text{list1 and list2}$ , create a list of the differences: Move the cursor to the name of an empty list, and then use VAR-LINK to enter the command $\text{list1}-\text{list2}$ . Press ENTER to perform the subtraction. Since inference for paired differences uses one-sample t -procedures, select $\text{2:T}-\text{Test or 2:}$ TIntervalfrom the STATTests or Intsmenu. Specify as your data the list of differences you just created, and apply the procedure. So, we have,

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

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

  $\begin{array}{l}P=0.0001\\ t=5.56\end{array}$

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,

  $P<0.05\Rightarrow \text{Reject }{H}_0$

Thus, we conclude that these data shows that European men are more likely than women to read newspaper.