A traffic engineer plans to estimate the average number of cars that pass through an intersection each day. Based on previous studies the standard deviation is believed to be 52 cars. She wants to estimate the mean to within ± 10 cars with 90 percent confidence. The needed sample size for n is:
eric's note book has 30 pages.he wants to write a number on each page. how many digits will he wite in his note book
n=8
To determine the needed sample size (n) to estimate the mean with a given confidence level and margin of error, you can use the following formula:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score (corresponding to the desired confidence level)
σ = standard deviation of the population
E = maximum allowable error (margin of error)
In this case, the standard deviation (σ) is known to be 52 cars, and the maximum allowable error (E) is ± 10 cars.
The Z-score corresponding to a 90% confidence level can be found using a standard normal distribution table or a statistical calculator. For a 90% confidence level, the Z-score is approximately 1.645.
Now we can calculate the sample size:
n = (1.645 * 52 / 10)^2
n ≈ 43.39^2
n ≈ 1886.52
Therefore, the needed sample size (n) is approximately 1887 cars (rounded up to the nearest whole number).
To determine the needed sample size (n) for estimating the mean with a desired level of confidence, we can use a formula that incorporates the desired margin of error, the standard deviation, and the confidence level.
In this case, the traffic engineer wants to estimate the mean number of cars passing through the intersection each day within ± 10 cars with 90% confidence. Here's how we can calculate the required sample size:
1. Identify the desired margin of error (E): In this example, the desired margin of error is ± 10 cars.
2. Determine the standard deviation (σ): According to previous studies, the standard deviation is believed to be 52 cars.
3. Calculate the critical value (Z): The confidence level is 90%, which means that the engineer wants to be 90% confident that the true mean falls within the margin of error. To find the critical value (Z), we can use a standard normal distribution table or a statistical calculator. For a 90% confidence level, the critical value (Z) is approximately 1.645.
4. Calculate the sample size (n):
n = (Z^2 * σ^2) / E^2
Plugging in the numbers:
n = (1.645^2 * 52^2) / 10^2
n = (2.703025 * 2704) / 100
n = 7308.552 / 100
n = 73.08552
Since the sample size needs to be a whole number, we should round up to the nearest whole number to ensure sufficient sample size.
Therefore, the needed sample size (n) is 74.