Question

The data given to the right includes data from

3838

​candies, and

66

of them are red. The company that makes the candy claims that

3131​%

of its candies are red. Use the sample data to construct a

9090​%

confidence interval estimate of the percentage of red candies. What do you conclude about the claim of

3131​%?

Answer 1

Let x be the number of red candies.

We are given x = 38 and n = 66

Therefore = x/n = 38/66 = 0.5758

given confidence level = 0.90

Therefore α = 1 - 0.90 = 0.1 , 1 - (α/2) = 0.95

We have to find z score corresponding to area 0.9500 on z score table

So z = 1.645

Confidence interval is given by,

=

=

0.4758 and 0.6758

90% confidence interval is ( 0.4758 , 0.6758 )

0.31 do not lies in the confidence interval , so we can conclude that the percentage of red candies are different that 31% .