In: Math
soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 98% confidence interval for the mean and are assuming that the population standard deviation for the number of soft drinks consumed each week is 1. The study found that for a sample of 898 adults the mean number of soft drinks consumed per week is 6.4. Construct the desired confidence interval. Round your answers to one decimal place. Lower and high endpoint
Solution :
Given that,
Point estimate = sample mean =
= 6.4
Population standard deviation =
= 1
Sample size = n = 898
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 * (1 / 898)
= 0.1
At 98% confidence interval estimate of the population mean is,
- E <
<
+ E
6.4 - 0.1 <
< 6.4 + 0.1
6.3 <
< 6.5
Lower endpoint = 6.3
High endpoint = 6.5