Compute a 95% confidence interval for the quantitative variable for the sales data set and interpret that interval.
Sales (Y) | |
Mean | 41.89 |
Standard Error | 0.84 |
Median | 43 |
Mode | 44 |
Standard Deviation | 8.39 |
Sample Variance | 70.32 |
Kurtosis | 1.66 |
Skewness | -0.45 |
Range | 46 |
Minimum | 21 |
Maximum | 67 |
Sum | 4189 |
Count | 100 |
We are asked to calculate and interpret the 95% confidence interval given the following data
Mean= 41.89
Standard Error= 0.84
Median= 43
Mode= 44
Standard Deviation= 8.39
Sample variance =70.32
Kurtosis= 1.66
Skewness = -0.45
Range= 46
Minimum= 21
Maximum= 67
Sum= 4189
Count= 100
The formula for 95% confidence interval for mean is,
(Mean-Z*Standard Error, Mean+Z*Standard Error)
where Z is the critical value at 5% significance level
The critical value at 5% significance level is 1.96.
Substituting the values in the given formula we get,
(41.89-1.96*0.84, 41.89+1.96*0.89)
=>(40.2436, 43.5364) is the required 95% confidence interval for the true mean of sales.
This means that we are 95% sure that the true average(or mean) of sales lies in the interval 40.2436 and 43.5364.
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