Question

An educator wishes to estimate the mean number of hours u that ten year old children in a certain city watch television per day. How large a sample is required if the educator wants to estimate μ within 0.5 hours with 95% confidence? Assume σ 1.5

(a) 5.0
(b) 34.6
(c) 35.0
(d) 25.0

Answer 1

Answer: (c) 35.0

Explanation:

We are given that ,

Margin of error : E= 0.5 hours

Standard deviation:
`\sigma= 1.5`

Confidence level : 95%

We know that the z-value for 92% confidence level is 1.96.

Now, the formula to find the sample size is given by :-

`n=((z* \sigma)/(n))^2`

Substitute all the value in this formula , we get

`n=((1.96*1.5)/(0.5))^2\\\\ n=(5.88)^2=34.5744\approx35`

[Rounded to the next whole number.]

Thus , the minimum sample size = 35.0

Hence the correct answer is option (c) 35.0