Question

1. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of n = 54 bears has a mean weight of ¯x = 182.9 lb and standard deviation of s = 121.8 lb. 86

(a) Calculate and interpret a 95% confidence interval estimate of the population mean µ bear weight.

(b) Find the length of the confidence interval constructed in part (a).

2. Hemoglobin levels in 11-year-old boys are normally distributed with unknown mean µ and standard deviation = 1.2 g/dL.

(a) Determine the sample size n needed to estimate population mean hemoglobin level with 95% confidence so that the margin of error E = 0.5 g/dL?

(b) Determine the sample size n needed to estimate population mean hemoglobin level with margin of error E = 0.5 g/dL with 99% confidence?

3.  A hospital administrator wished to estimate the average number of days µ
required for treatment of patients between the ages of 25 and 34. A random
sample of n = 35 hospital patients between these ages produced a sample mean
x¯ = 5.4 days and sample standard deviation s = 3.1 days.
(a) Calculate and interpret a 95% confidence interval for the mean length of stay µ for the population of patients from which the sample was drawn.
(b) Determine the length of the interval from part (a).
(c) Calculate and interpret a 99% confidence interval for the mean length of stay µ for the population of patients from which the sample was drawn.
(d) Determine the length of the interval from part (c).
(e) Why is the interval obtained in part (c) wider than that obtained in part (a)?

Answer 1

Solution-:

Q.1 Given:

(a) The 95% confidence interval estimate of the population mean µ bear weight is,

(By using MS-Excel Command "=TINV(0.05,53)")

Here, Degree of freedom

The required 95 % C.I. is

(b) Legnth of C.I =

Q.2 Given: Hemoglobin levels in 11-year-old boys are normally distributed with unknown mean µ and standard
  deviation =  

(a) Also 95% C.I. and Margin of error

Here, (Using Z- table)

(b) Also 99% C.I. and Margin of error

Here,   (Using Z- table)