Question

400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct
| a hypothesis test to check whether this represents a statistically significant difference from 50%, and use a
| significance level of 0.01.

Use qnorm(alpha/2) to find -z(alpha/2)

Answer 1

Solution :

n = 400

x = 289 , p^ = x/n = 289/400 = 0.7225

x: number of students did not get enough sleep.

Null Hypothesis Ho : p= 0.5 ; Alternative Hypothesis Ha : p ≠ 0.5
α = significance level of 0.01

Test Statistic = (p^ - p)/√(p(1-p)/n) = (0.7225-0.5)/√(0.5*0.5)/400) = 8.90

The critical value = z(alpha/2) = -qnorm(alpha/2) = -qnorm(0.005) = 2.575829

Here test statistic value (8.90) is greater than critical value (2.575829) Hence we reject Ho

Conclusion: At 0.01 level of significance we have statistically significant difference from 50%