Answer:
Population: The population is the total demand (sale) of the product over all days.
Variable of interest: The variable of interest is the daily demand (sale) of the product.
To obtain the confidence interval for the average daily demand at a confidence level of 97%, we can use the following formula:
Confidence interval = sample mean ± (t-value x standard error)
where t-value is the value from the t-distribution for the desired confidence level and degrees of freedom, and the standard error is calculated as:
standard error = sample standard deviation / √n
where n is the sample size.
Using the given data, we can calculate:
Sample mean = (35+44+38+55+33+56+60+45+48+40+45+35+42)/12 = 44.5
Sample standard deviation = 9.92
Degrees of freedom = n-1 = 12-1 = 11
From the t-distribution table with 11 degrees of freedom and a confidence level of 97%, the t-value is approximately 2.718.
Therefore, the confidence interval for the average daily demand is:
Confidence interval = 44.5 ± (2.718 x 9.92/√12) = 44.5 ± 9.14
The lower limit is 44.5 - 9.14 = 35.36 and the upper limit is 44.5 + 9.14 = 53.64.
So, we can say with 97% confidence that the true population average daily demand falls within the range of 35.36 to 53.64 thousand units.