Question

As the price of oil rises, there is increased worldwide interest in alternate sources of energy. An NGO surveyed people in two countries to assess attitudes toward different forms of alternative energy. The data in the table below represent the survey's findings concerning whether people favor or oppose the building of new nuclear power plants.

Table 1 Observed Frequencies

	Country
Response	France	Italy
Favor	23	32
Oppose	39	19
No opinion	17	30

1. How large was the sample in this poll?
2. Construct a table of expected frequencies for alternative energy preference by country.
3. Conduct a hypothesis test at a 5% level of significance to determine whether people’s attitudes toward building new nuclear plants is independent of their country? What is your conclusion?
4. Does your answer change at a 1% level of significance?

Answer 1

I have used Minitab to answer the question. Please find below output

Tabulated Statistics: Response, Worksheet columns 

Rows: Response   Columns: Worksheet columns

              France  Italy     All

Favor             23     32      55
               14.38  20.00   34.38

Oppose            39     19      58
               24.38  11.88   36.25

No Opinion        17     30      47
               10.63  18.75   29.38

All               79     81     160
               49.38  50.63  100.00

Cell Contents:      Count
                    % of Total


Pearson Chi-Square = 11.942, DF = 2, P-Value = 0.003
Likelihood Ratio Chi-Square = 12.138, DF = 2, P-Value = 0.002

a)

Response    France  Italy   Row Total
Favor         23          32       55
Oppose        39          19       58
No Opinion        17      30       47
Column Total  79          81       160 = Grand Total

The total number of responses = 160.

b)

Expected Freq. (France)   Expected Freq. (Italy)
27.16 27.84
28.64 29.36
23.21 23.79

c) Here,

Null hypothesis is (H0): People’s attitude toward building new nuclear power plants is independent of the country.

Vs

Alternative Hypothesis (H1): People’s attitude toward building new nuclear power plants is not independent of the country.

By looking at the p-value is 0.003 which is less than 0.05 hence we reject the null hypothesis i.e. People’s attitude toward building new nuclear power plants is not independent of the country.

d)

Yes, the answer changes when we consider the 0.01 level of significance and in this case, we accept null hypothesis i.e. People’s attitude toward building new nuclear power plants is independent of the country.