Question

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

Answer 1

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.