Question

In a recent statistics survey, 37 out of 129 randomly sampled college students said they get enough sleep. Penn State conducted a much larger scale study a few years ago and found that 40% of college students got enough sleep. Is the lower percentage among college students in the recent study due to chance or is it signifcantly lower than the Penn State study? Determine the alpha level for this study.

Answer 1

This is a test for binomial proportion since the answers by the students could have only 2 possible ans that they get enough sleep or not.

x : No. getting enough sleep

x = 37 n=129

The sample proportion

= 0.2868

We want to test whether students has lower than 40% of students not getting enough sleep

Since 'n' is large we can use normal approximation

Test

: The proportion of students getting sleep = 40%

p = 40%

: The proportion of students getting sleep is lower than 40%

p < 40%

This is a one tailed test.

Test Stat =

=

Test Stat = -2.624

We will take level of significance of 5%

Critical value at 5%

= 1.6449 ..........................found using normal percentage tables

Since |Test Stat| > Critical value

We reject the null hypothesis at 5%.

We conclude that the percentage among college students is significantly lower than the Penn State study.