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A museum wants to determine the fee that should be charged the visiter to enable it to earn revenue rs 40 million per annum. The museum has estimated that 500 visiter visit daily. The size of sample that needed 95%confidence level the claim does not exceed 25 population standard deviation is 60.?
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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.
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.
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A museum wants to determine the fee that should be charged the visiter to enable it to earn revenue rs 40 million per annum. The museum has estimated that 500 visiter visit daily. The size of sample that needed 95%confidence level the claim does not exceed 25 population standard deviation is 60.?
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A museum wants to determine the fee that should be charged the visiter to enable it to earn revenue rs 40 million per annum. The museum has estimated that 500 visiter visit daily. The size of sample that needed 95%confidence level the claim does not exceed 25 population standard deviation is 60.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A museum wants to determine the fee that should be charged the visiter to enable it to earn revenue rs 40 million per annum. The museum has estimated that 500 visiter visit daily. The size of sample that needed 95%confidence level the claim does not exceed 25 population standard deviation is 60.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A museum wants to determine the fee that should be charged the visiter to enable it to earn revenue rs 40 million per annum. The museum has estimated that 500 visiter visit daily. The size of sample that needed 95%confidence level the claim does not exceed 25 population standard deviation is 60.?.
A museum wants to determine the fee that should be charged the visiter to enable it to earn revenue rs 40 million per annum. The museum has estimated that 500 visiter visit daily. The size of sample that needed 95%confidence level the claim does not exceed 25 population standard deviation is 60.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A museum wants to determine the fee that should be charged the visiter to enable it to earn revenue rs 40 million per annum. The museum has estimated that 500 visiter visit daily. The size of sample that needed 95%confidence level the claim does not exceed 25 population standard deviation is 60.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A museum wants to determine the fee that should be charged the visiter to enable it to earn revenue rs 40 million per annum. The museum has estimated that 500 visiter visit daily. The size of sample that needed 95%confidence level the claim does not exceed 25 population standard deviation is 60.?.
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