P-value Statistics question!!!

Question

In an opinion survey, the proportion of city residents in favor of a tax increase was p=158/300=.527. The resulting P-value was .18. Interpret the P-value in context.

 

A)Only 18% of the city residents support the tax increase.

B) There is an 18% chance that the majority of residents support the tax increase.

C)Assuming that 50% of residents support the tax increase, there is an 18% probability that the sample proportion would be .527 or higher by chance alone.

D) Assuming that 50% of residents support the tax increase, there is an 18% chance that the null hypothesis is true by chance alone.

 

Answer 1

By definition the P-value is the probability, computed assuming the null hypothesis is true, that the observed outcome would take a value as extreme or more extreme than that actually observed.  They don't say in the question what the null hypothesis was, but you can infer from the possible answers that it must have been that 50% of residents support the tax increase.  They also don't say what the alternative hypothesis was (it could have been one sided (p is greater than 50%) or two sided (p is not equal to 50%)).  If it was one sided then there is an 18% probability, assuming that 50% of the residents support the tax increase, that the sample proportion would be .527 or higher by chance alone.