Question

Sheila's measured glucose level one hour after a sugary drink varies according to the Normal distribution with μμ = 130 mg/dl and σσ = 15 mg/dl. What is the level L such that there is probability only 0.15 that the mean glucose level of 4 test results falls above L?

L=

A study of the career paths of hotel general managers sent questionnaires to an SRS of 210 hotels belonging to major U.S. hotel chains. There were 88 responses. The average time these 88 general managers had spent with their current company was 12.7 years. (Take it as known that the standard deviation of time with the company for all general managers is 3.6 years.)

(a) Find the margin of error for an 85% confidence interval to estimate the mean time a general manager had spent with their current company:  years

(b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company:  years

(c) In general, increasing the confidence level  the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)

Answer 1

Solution,

Given that,

1) mean = = 130

standard deviation = = 15

n = 4

= = 130

= / n = 15 / 4 = 7.5

Using standard normal table,

P(Z > z) = 0.15

= 1 - P(Z < z) = 0.15  

= P(Z < z ) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.036) = 0.85  

z = 1.036

Using z-score formula  

= z * +

= 1.036 * 7.5 + 130

= 137.77

L = 138 mg / dl

2) Given that,

Point estimate = sample mean = = 12.7

Population standard deviation =    = 3.6

Sample size = n = 88

a) At 85% confidence level

= 1 - 85%  

= 1 - 0.85 =0.15

/2 = 0.075

Z/2 = Z_0.075 = 1.44

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

E = 1.44 * ( 3.6 /  88)

E = 0.55

b) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.576

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

E = 2.576 * ( 3.6 /  88)

E = 0.99

(c) In general, increasing the confidence level ''INCREASES''  the margin of error (width) of the confidence interval.