Question

1. In a sample of 10 packages of hamburger buns, the average (mean) weight of the packages was 200 grams. Assuming that the population standard deviation is 2.5 grams, construct a 92% confidence interval. [Show ALL your work. No marks will be awarded without supporting calculations]

2.In a sample of 35 packages of hot dogs, the average (mean) weight of the packages was 454 grams and the sample standard deviation was 20 grams. Construct a 98% confidence interval. [Show ALL your work. No marks will be awarded without supporting calculations]

Answer 1

1)

Solution :

Given that,

Point estimate = sample mean = = 200

Population standard deviation = = 2.5

Sample size = n = 10

At 92% confidence level the z is ,

= 1 - 92% = 1 - 0.92 = 0.08

/ 2 = 0.08 / 2 = 0.04

Z/2 = Z0.04 = 1.751

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

= 1.751 * ( 2.5/ 10 )

= 1.38

At 99% confidence interval estimate of the population mean is,

- E < < + E

200 - 1.38 < < 200 + 1.38

198.62 < < 201.38

( 198.62 , 201.38 )

2)

Given that,

Point estimate = sample mean = = 454

Population standard deviation = = 20

Sample size = n = 35

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z/2 = Z0.01 = 2.326

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

= 2.326 * ( 20/ 35 )

= 7.86

At 98% confidence interval estimate of the population mean is,

- E < < + E

454 - 7.86 < < 454 + 7.86

446.14 < < 552.86

(446.14 , 552.86)