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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

Respuesta :

Answer:

The sample size should be approximately 167.

Step-by-step 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:

[tex]\text{Marginal error} = z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]

Ptting values, we get,

[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 2.58[/tex]

[tex]10 = 2.58\times \dfrac{50}{\sqrt{n}}\\\\n = \bigg(\dfrac{2.58\times 50}{10}\bigg)^2\\\\n = 166.41\approx 167[/tex]

The sample size should be approximately 167.