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

Step-by-step 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 :-

$n=(\dfrac{z\times \sigma}{n})^2$

Substitute all the value in this formula , we get

$n=(\dfrac{1.96\times1.5}{0.5})^2\\\\ n=(5.88)^2=34.5744\approx35$

[Rounded to the next whole number.]

Thus , the minimum sample size = 35.0

Hence the correct answer is option (c) 35.0