Question

How do I find the margin of error with a 98% confidence interval estimate of the population mean sales price and population mean number of days to sell for Domestic cars?

For Domestic Cars
Statistics
		List Price	Sale Price	Days to Sell
N	Valid	200	200	200
	Missing	0	0	0
Mean		32.1615	29.7430	32.9050
Median		29.5500	27.5500	31.0000
Std. Deviation		18.31094	18.25088	17.86735
Range		75.00	74.60	69.00

Answer 1

Since the sample size N=200 is greater than 30, we will use normal distribution as the sampling distribution of mean.

The right tail critical value for 98% confidence interval, with significance level calculated using

Using the standard normal tables, we can get for z=2.33, we get P(Z<2.33)=0.99

Hence the right tail critical value for 98% confidence interval is (we are rounding this to 2 decimals, if you need higher precision use Excel/calculator)

The margin of error is calculated using

where is the standard error of mean.

1. Sale price

The sample size is N=200

is the sample mean sale price

We know the sample standard deviation of the sale price as

Using this we can estimate the population standard deviation of sale price as

The estimated standard error of mean is

The margin of error with a 98% confidence interval estimate of the population mean sales price is

ans: The margin of error with a 98% confidence interval estimate of the population mean sales price is 3.0069 (mention the units, for example in $1000s)

98% confidence interval estimate of the population mean sales price is

ans: 98% confidence interval estimate of the population mean sales price is [26.7361, 32.7499] (in $1000s ?)

2. Days to sell

The sample size is N=200

is the sample mean Days to sell

We know the sample standard deviation of the Days to sell as

Using this we can estimate the population standard deviation of Days to sell as

The estimated standard error of mean is

The margin of error with a 98% confidence interval estimate of the population mean Days to sell is

ans: The margin of error with a 98% confidence interval estimate of the population mean Days to sell is 2.9438 (mention the units, for example, days)

98% confidence interval estimate of the population mean Days to sell is

ans: 98% confidence interval estimate of the population mean Days to sell is [29.9612,35.8488] days