Question

3. a) The amount of time it takes you to fall asleep is called “sleep latency”. Sleep latency in adults is Normal with a standard deviation of 3.5 minutes. Forty-nine healthy adults volunteered for a sleep study, where their sleep was monitored for one night. The volunteers had an average sleep latency of 17.1 minutes.

i. Compute the 80% confidence interval for the parameter of interest in this study.

ii. Interpret the previously computed interval in the context of the question

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 17.1

Population standard deviation =    = 3.5

Sample size n =49

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.10

Z/2 = Z0.10= 1.28 ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.28 * ( 3.5 / 49  )

= 0.64
At 80% confidence interval estimate of the population mean
is,

- E < < + E

17.1 - 0.64 <   < 17.1 +0.64

16.46<   < 17.74

( 16.46, 17.74 )