Suppose a survey of 240 college students finds that 147 say they are not getting enough sleep construct a 95% confidence interval for the proportions of college students who are not getting enough sleep what is the lower end of the confidence interval answer as a decimal round at least 3 places

 

Suppose a survey of 240 college students finds that 147 say they are not getting enough sleep.

So we will let p be the proportion of college students who are not getting enough sleep.

• p = 147/240
• p = 0.6125
• Sample size, n = 240

The 95% confidence interval for the proportions of college students who are not getting enough sleep is calculated by the formula:

• p₀ = p ± z*sqrt(p(1-p)/n)

Where at 95% confidence, z = 1.96, so;

• p₀ = 0.6125 ± 1.96*sqrt(0.6125(1-0.6125)/240)
• p₀ = 0.6125 ± 0.0616367
• p₀ = 0.55086 and 0.674137

The 95% confidence interval is between 0.55086 and 0.674137.

(Round your final answer to the required decimals.)

The lower end of the confidence interval is 0.55086 with upper end 0.674137.