Question

A simple random sample of 10 households, the number of TV's that each household had is as follows: 2 , 0 , 2 , 2 , 2 , 2 , 1 , 5 , 3 , 2 Assume that it is reasonable to believe that the population is approximately normal and the population standard deviation is 0.55 . What is the lower bound of the 95% confidence interval for the mean number of TV's?

Answer 1

Answer: 1.758 is the lower bound of the 95% confidence interval for the mean number of TV's.

Explanation:

Given that,

n = 10

Number of TV each household have = {2 , 0 , 2 , 2 , 2 , 2 , 1 , 5 , 3 , 2}

Standard Deviation(SD) = 0.55

95% Confidence Interval, = 0.05

Follows normal distribution,

Mean =
`\bar{X} = (2+0+2+2+2+2+1+5+3+2)/(10)`

=
`(21)/(10)`

= 2.1

Therefore, 95% Confidence Interval are as follows:

`\bar{X}\pm Z_{(\alpha)/(2)} * (\sigma)/(√(n))`

`2.1\pm 1.96 * (\0.55)/(√(10))`

Hence,

Lower bound = 2.1- 1.96 ×
`(\0.55)/(√(10))`

= 2.1- 1.96 × 0.174

= 1.758