Question

Does college experience depend on a major? The mean satisfaction with college experience in a random sample of 61 sociology majors is 8.5 with a standard deviation of 1.5. The mean satisfaction with college experience of all students is 8.0. Are sociology majors DIFFERENT from all other students in terms of their college satisfaction? Round your answers to two decimal places. Use 0.01 for alpha.

Answer 1

Given that, sample size (n) = 61

sample mean $(\bar x)$ = 8.5

standard deviation = 1.5

The null and alternative hypotheses are,

H0 : μ = 8.0

Ha : μ ≠ 8.0

critical values at significance level of 0.01 are, Z_{​​​​​​crit} = ± 2.58

Rejection region : Z < -2.58 or Z > 2.58

Test statistic is,

$Z = \frac { 8.5-8.0}{\frac { 1.5}{\sqrt {61}}} = 2.60$

=> Test statistic = 2.60

Since, test statistic = 2.60 > 2.58, we should reject the null hypothesis.