In: Statistics and Probability
1. Explain with words and steps how to create a confidence
interval for estimating the true value of the population mean of
the number of cars owned by Beverly Hills households. Don't forget
to write an interpretation of the confidence interval. The sample
results were:
a. Sample size of 100 people.
a. Sample average was 5.2.
a. Sample standard deviation was 2.8.
Please don't hesitate to give a thumbs up for the answer in case you are satisfied with it.
To find the confidence interval do the following:
1. Find the critical test statistic for the confidence level. Take the alpha , divide it by 2, add 0.5 to it to get the cumulative probability. Use appropriate Z or T table to get the the critical statistic. If you have the confidence level alpha is 1- confidence level.
2. Next calculate margin error. It is the critical statistic you calculate in step 1 times the standard deviation of sample divided by square root of sample size. For us it is = t*2.8/sqrt(100) or 0.28*t
3. Calculate the confidence interval as
Sample average +/- Margin of error
= 5.2 +/- 0.28*t
Interpretation: The confidence level tells us the long-term capture rate of these intervals over repeated samples. In other words , with x percentage confidence you can say that the true population mean of number of cars Beverly Hills household own lies between the interval mentioned above.