Question

In a recent year, 65% of first-year college students responding to a national survey identified "being very well-off financially" as an important personal goal. A state university finds that 102 of an SRS of 200 of its first-year students say that this goal is important. Is there convincing evidence at the α=0.05 significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value, 65%?

Answer #1

H0: p = 0.65

Ha: p 0.65

Sample proportion = 102 / 200 = 0.51

Test statistics

z = ( - p ) / sqrt [ p ( 1 - p) / n

= ( 0.51 - 0.65) / sqrt ( 0.65 ( 1 - 0.65) / 200 ]

= -4.15

From Z table,

critical values at 0.05 level = -1.96 , 1.96

Since test statistics falls in rejection region, that is z < -1.96 , Reject H0.

We have sufficient evidence to conclude that the proportion of all first-year students at this university

who think being very well-off is important differs from the national value 65%

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