What type of test is it ? Left tail , right tail , or two tail

Question

A politician claims that the majority of americans approve of a public health care option. A survey of 500 randomly selected adults found that 346 approve of a public health care option. 

Answer 1

Jakirah,

 

If there was no difference in the proportion of those who approve and those who disapprove, then p₀ (the population proportion) would equal .50 (half approve, half disapprove). In a normal distribution, the .5 would lie in the middle of the curve with proportions less than .5 to the left and those greater than .5 to the right.

 

The null hypothesis for the test is just that: the sample proportion, p, equals the population proportion, p₀.  We write this as:

 

H₀: p = p₀

 

The alternative hypothesis would state that (1) the sample proportion is not equal to the population proportion (H_a: p ≠ p₀); a two-tailed test, (2) that the sample proportion is greater than the population proportion (H_a: p > p₀); a right-tailed test, or (3) that the sample proportion is less than the population proportion (H_a: p < p₀); a left-tailed test.

 

The problem states the claim that the majority of American approve (so the sample proportion must be greater than the population proportion).

 

What we have, then is right tailed test to do since the hypothesis states that we should find a sample proportion greater than the population's (that is, greater than .50). 346/500 is greater than .50.