Question

An annual survey of​ first-year college students asks 273 comma 000 students about their attitudes on a variety of subjects. According to a recent​ survey, 57​% of​ first-year students believe that abortion should be legal. Use a 0.05 significance level to test the claim that over half of all​ first-year students believe that abortion should be legal. Formulate the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0​: pequals0.5 Upper H Subscript a​: pgreater than0.5 B. Upper H 0​: pequals0.5 Upper H Subscript a​: pnot equals0.5 C. Upper H 0​: pless than0.5 Upper H Subscript a​: pequals0.5 D. Upper H 0​: pequals0.5 Upper H Subscript a​: pless than0.5

Answer 1

Since the claim that over half of all​ first-year students believe that abortion should be legal so

So option is:

A. Upper H0​: p equals 0.5 Upper H Subscript a​: p greater than 0.5

p=population proportion.

Test and CI for One Proportion

Test of p = 0.5 vs p > 0.5

95% Lower
Sample X N Sample p Bound Z-Value P-Value
1 155610 273000 0.570000 0.568441 73.15 0.000

Using the normal approximation.

Since p-value<0.05 so we reject the null hypothesis and conclude that  over half of all​ first-year students believe that abortion should be legal.