Question

Morgan sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. using a 90% confidence level, she also found that t* = 1.660. c o n f i d e n c e space i n t e r v a l space equals space x with bar on top plus-or-minus t asterisk times space bevelled fraction numerator s over denominator square root of n end fraction a 90% confidence interval calculates that the average number of hours of sleep for working college students is between __________ hours. answer choices are rounded to the hundredths place.

Answer 1

The average number of hours of sleep for working college students is between 6.85 and 6.15 hours

Explanation:

We are given,

Average = M = 6.5

Standard Deviation = S = 2.14

t = 1.660

sample size = n = 101

So,

(t)(S)/(√n) = (1.660)(2.14)/√(101)

= 0.3535

Now,

The confidence interval is,

CI = M ± (t)(S)/(√n)

CI = 6.5 ± 0.3535

Upper limit = 6.5 + 0.3535

Upper limit = 6.85 hours

Lower limit = 6.5 - 0.3535

Lower limit = 6.15 hours

Hence,

the average number of hours of sleep for working college students is between 6.85 and 6.15 hours