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 of 65%?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p =0.65

H_a : p 0.65

= x / n = 102 / 200 = 0.51

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.51 - 0.65 / [(0.65 * 0.35) / 200]

= -4.15

P-value = 0.000

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that the proportion of all first-year students at this

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