Question

TheCurdleDairyCo.wantstoestimatetheproportionpofcustomersthat will purchase its new broccoli-flavored ice cream. Curdle wants to be 92% confident that they have estimated p to within .05. How many customers should they sample?

6. Foracertainurbanarea,inasampleof5months,anaverageof28mail carriers were bitten by dogs each month. The standard deviation of the population is 3 mail carriers. Find the 90% confidence interval of the true mean number of mail carriers who are bitten by dogs each month.

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 0.05

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

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.751/0.05 )2 * 0.5 * 0.5

= 306.60

sample size = 307

6)

Given that,

Point estimate = sample mean = = 28

Population standard deviation = = 3

Sample size = n = 5

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (3 / 5 )

= 2.21

At 90% confidence interval estimate of the population mean is,

- E < < + E

28 - 2.21 < < 28 + 2.21

25.79 < < 30.21

( 25.79 , 30.21 )