Question

CH 8

1.

A simple random sample of 900 individuals provides 300 Yes responses.

a. What is the point estimate of the proportion of the population that would provide Yes responses (to 3 decimals, if needed)?  

b. What is your estimate of the standard error of the proportion (to 4 decimals)?  

c. Compute the 95% confidence interval for the population proportion (to 3 decimals).
( ,  )

2.

A simple random sample of 60 items resulted in a sample mean of 67. The population standard deviation is 12.

a. Compute the 95% confidence interval for the population mean (to 1 decimal).

(  ,   )

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).

(  ,   )

Answer 1

Solution :

1) Given that,

a) Point estimate = sample proportion = = x / n = 300 / 900 = 0.333

1 - = 1 - 0.333 = 0.667

b) =  [p ( 1 - p ) / n] =   [(0.333 * 0.667) / 900 ] = 0.0157

c) Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.333 * 0.667) / 900)

= 0.031

A 95% confidence interval for population proportion p is ,

± E

= 0.333  ± 0.031

= ( 0.302, 0.364 )

2) Given that,

a) Z/2 = Z0.025 = 1.96

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

= 1.96 * ( 12 /  60 )

= 3.04

At 95% confidence interval estimate of the population mean is,

  ± E

= 67  ± 3.04

= ( 63.96, 70.04 )

b) Z/2 = Z0.025 = 1.96

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

= 1.96 * ( 12 /  120 )

= 2.15

At 95% confidence interval estimate of the population mean is,

  ± E

= 67  ± 2.15

= ( 64.85, 69.15 )