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A random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population?
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A random sample of height of hundred during form a lot of a nation of ...
Understanding Confidence Intervals
Confidence intervals provide a range of values that likely contain the true population parameter. In this case, we're estimating the average height of students based on a sample.
Given Data
- Sample size (n): 100
- Sample mean (x̄): 1.75 meters
- Standard deviation (σ): 0.35 meters
- Confidence level: 95%
Calculating the Confidence Interval
1. **Determine the Z-value**
For a 95% confidence level, the Z-value (critical value) is approximately 1.96.
2. **Calculate the Standard Error (SE)**
The standard error of the mean is calculated using the formula:
SE = σ / √n
SE = 0.35 / √100
SE = 0.35 / 10
SE = 0.035
3. **Compute the Margin of Error (ME)**
The margin of error is found by multiplying the Z-value by the standard error:
ME = Z * SE
ME = 1.96 * 0.035
ME = 0.0686 (approx.)
4. **Determine the Confidence Interval**
The confidence interval is given by:
Lower Limit = x̄ - ME
Upper Limit = x̄ + ME
Lower Limit = 1.75 - 0.0686 ≈ 1.6814
Upper Limit = 1.75 + 0.0686 ≈ 1.8186
Final Result
At a 95% confidence level, the average height of students in the population is estimated to be between approximately **1.6814 meters** and **1.8186 meters**. This means we can be 95% confident that the true average height falls within this range.
Confidence intervals provide a range of values that likely contain the true population parameter. In this case, we're estimating the average height of students based on a sample.
Given Data
- Sample size (n): 100
- Sample mean (x̄): 1.75 meters
- Standard deviation (σ): 0.35 meters
- Confidence level: 95%
Calculating the Confidence Interval
1. **Determine the Z-value**
For a 95% confidence level, the Z-value (critical value) is approximately 1.96.
2. **Calculate the Standard Error (SE)**
The standard error of the mean is calculated using the formula:
SE = σ / √n
SE = 0.35 / √100
SE = 0.35 / 10
SE = 0.035
3. **Compute the Margin of Error (ME)**
The margin of error is found by multiplying the Z-value by the standard error:
ME = Z * SE
ME = 1.96 * 0.035
ME = 0.0686 (approx.)
4. **Determine the Confidence Interval**
The confidence interval is given by:
Lower Limit = x̄ - ME
Upper Limit = x̄ + ME
Lower Limit = 1.75 - 0.0686 ≈ 1.6814
Upper Limit = 1.75 + 0.0686 ≈ 1.8186
Final Result
At a 95% confidence level, the average height of students in the population is estimated to be between approximately **1.6814 meters** and **1.8186 meters**. This means we can be 95% confident that the true average height falls within this range.
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A random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population?
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A random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population? 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 random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population?.
A random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population? 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 random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population?.
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