An annual survey of first year college students asks 276000 students about their

Question

An annual survey of first year college students asks 276000 students about their attitudes on a variety of subjects. According to a recent survey, 55% 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. Find the test statistic and the p value. An annual survey of first year college students asks 276000 students about their attitudes on a variety of subjects. According to a recent survey, 55% 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. Find the test statistic and the p value.

Explanation / Answer

Null and Alternative Hypothesis:

H0: P = 0.50

H1: P > 0.5

Level of significance:

a = .05

z = (p^ - P) / sqrt ((P*(1-P))/n)

   = (0.55-0.5)/sqrt(0.5*(1-0.5))/276000)

   = 52.54

The value of the test statistics is 52.54

The p-value = P ( z > 52.54 )

By using Normal Distribution Table we get,

P ( z > 52.54 ) = 0

The p-value is approximately 0.

P-value is less than the level of significance (0 < .05); the null hypothesis can be rejected.

At 5% level of significance there is sufficient evidence to conclude that over half of all first year students believe that abortion should be legal.

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