Question

Dairy Products Unlimited is studying the characteristics of the ice cream industry in Brazil.  They take a random sample of 20 ice cream manufacturers in order to assess the average number of flavors currently marketed by Brazilian manufacturers.  The mean is 5.2 and the standard deviation is 0.9.  Find a 95% confidence interval for the population mean number of flavors.

1. What do I know?  

2. What do I want to find out?

3. How do I go from what I know to what I want to find?

4. Does the answer make sense?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 5.2

sample standard deviation = s = 0.9

sample size = n = 20

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,19 = 2.093

Margin of error = E = t/2,df * (s /n)

= 2.093 * (0.9 / 20)

Margin of error = E = 0.42

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

  ± E  

= 5.2   ± 0.42

= ( 4.78, 5.62 )