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It is desired to estimate the daily demand (sale) of a product registered by a company. For this, 12 days are selected at random with the following values in thousands for the demand

35, 44, 38, 55, 33, 56, 60, 45, 48, 40, 45, 35,42
Determine the population, the variable of interest and obtain the confidence interval for the average daily demand at a confidence level of 97%.

User Randoms
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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.

User Stanislas Morbieu
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