Question

The NJ Department of Highways wants to estimate the average number of the passenger cars that pass a busy intersection of R1 each day. The requirements are that the estimate be within t.10 cars per day of the population mean and that the investigators be 99% confident of the results. A similar study showed that the standard deviation to be 50 cars per day. How large a sample is required? a) 13 b) 67 c) 52 d) 161 e) 167

Answer 1

The sample size should be approximately 167.

Explanation:

We are given the following in the question

Sample size, n = 10

Confidence level = 99%

Significance level = 0.01

Standard deviation, σ = 50

Error = 10

Formula:

`\text{Marginal error} = z_(critical)(\sigma)/(√(n))`

Ptting values, we get,

`z_(critical)\text{ at}~\alpha_(0.05) = \pm 2.58`

`10 = 2.58* (50)/(√(n))\\\\n = \bigg((2.58* 50)/(10)\bigg)^2\\\\n = 166.41\approx 167`

The sample size should be approximately 167.