n a transportation study of 20 large cities, it was found that the mean of the number of cars per person was 0.504. (Some of the people in the city are children.) The study also stated that the standard deviation s was 0.123. Find a 95 % confidence interval for the true mean number of cars per person.

Question

n a transportation study of 20 large cities, it was found that the mean of the number of cars per person was 0.504. (Some of the people in the city are children.) The study also stated that the standard deviation s was 0.123. Find a 95 % confidence interval for the true mean number of cars per person.

Answer 1

95% = mean ± 1.96 SEm

SEm = SD/√n

Answer 2

I am so lost I know the mean is 0.504 so is the SEM 1.96?

Answer 3

To find a 95% confidence interval for the true mean number of cars per person, we can use the formula:

Confidence Interval = Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))

First, let's determine the critical value. Since we want a 95% confidence interval, we need to use the corresponding Z-score.

The Z-score for a 95% confidence interval is 1.96. This value can be obtained from standard normal distribution tables or using statistical software.

Now, we have all the necessary information to calculate the confidence interval:

Confidence Interval = 0.504 ± (1.96) * (0.123 / √(20))

Calculating the value within the parentheses:

(1.96) * (0.123 / √(20)) ≈ 0.054

Now, we can substitute this value into the formula:

Confidence Interval = 0.504 ± 0.054

Therefore, the 95% confidence interval for the true mean number of cars per person is approximately (0.450, 0.558).

This means that we are 95% confident that the true mean number of cars per person falls between 0.450 and 0.558, based on the given data from the transportation study.