A museum wants to determine the fee that should be charged the visiter...
Determining Museum Fees
Size of Sample
- A sample size of visitors needs to be determined in order to estimate the average fee that should be charged to visitors.
- The sample size can be determined using a confidence level of 95%, a population standard deviation of 60, and a claimed revenue of Rs 40 million per annum.
- The formula to determine sample size is:
n = (Z^2 * σ^2) / E^2
Where:
n = sample size
Z = confidence level (1.96 for 95% confidence level)
σ = population standard deviation
E = margin of error
- Plugging in the values, we get:
n = (1.96^2 * 60^2) / 25^2
n ≈ 55
- Therefore, a sample size of 55 visitors is needed to estimate the average fee that should be charged to visitors.
Estimating the Average Fee
- Once the sample size has been determined, the museum can collect data on the fees paid by the visitors in the sample.
- Using this data, the museum can calculate the sample mean and standard deviation.
- The formula to determine the sample mean is:
x̄ = Σx / n
Where:
x̄ = sample mean
Σx = sum of all values in the sample
n = sample size
- The formula to determine the sample standard deviation is:
s = √[Σ(x - x̄)^2 / (n - 1)]
Where:
s = sample standard deviation
x = individual value in the sample
x̄ = sample mean
n = sample size
- With the sample mean and standard deviation calculated, the museum can estimate the average fee that should be charged to visitors.
- The formula to estimate the average fee is:
x̄ ± t*(s/√n)
Where:
x̄ = sample mean
s = sample standard deviation
n = sample size
t = t-value from the t-distribution table
- The t-value is determined based on the degrees of freedom, which is equal to the sample size minus one.
- Using a 95% confidence level and a sample size of 55, the t-value from the t-distribution table is approximately 2.008.
- Plugging in the values, we get:
x̄ ± 2.008*(s/√n)
- Assuming the museum wants to earn Rs 40 million per annum and 500 visitors visit daily, we can estimate the average fee that should be charged to visitors.
- If we assume the sample mean is Rs 80 and the sample standard deviation is Rs 20, we get:
80 ± 2.008*(20/√55)
80 ± 5.56
Rs 74.44 to Rs 85.56
- Therefore, the museum should charge an average fee of approximately Rs 75 to Rs 86 to earn Rs 40 million per annum.
A museum wants to determine the fee that should be charged the visiter...
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