In a random sample of 200 Americans, 51% said they favor building more nuclear power plants. In a random sample of 150 French, 48% said they favor building more nuclear power plants. At? = 0.10, is there enough evidence to say the proportions are the same?

Yes, there is enough evidence to say the proportions are the same.

Step-by-step explanation:

Null hypothesis: The proportions are the same.

Alternate hypothesis: The proportions are not the same.

Data given:

p1 = 51% = 0.51

n1 = 200

p2 = 48% = 0.48

n2 = 150

pooled proportion (p) = (n1p1 + n2p2) : (n1 + n2) = (200*0.51 + 150*0.48) : (200 + 150) = 174 : 350 = 0.497

Test statistic (z) = (p1 - p2) : sqrt[p (1-p) (1/n1 + 1/n2) = (0.51 - 0.48) : sqrt[0.497 (1-0.497) (1/200 + 1/150) ] = 0.03 : 0.054 = 0.556

The test is a two-tailed test. At 0.10 significance level the critical values - 1.645 and 1.645

Conclusion:

Fail to reject the null hypothesis because the test statistic 0.556 falls within the region bounded by the critical values.