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An article gave the following observations on maximum concrete pressure (kN/m²):

33.3, 41.8, 37.4, 40.3, 36.7, 39.2, 36.3, 41.9, 36.0, 35.3, 36.8, 38.9, 35.8, 35.3, 40.1

Calculate an upper confidence bound with a confidence level of 95% for the population standard deviation of maximum pressure. Round to four decimal places.

Answer :

Final answer:

The upper confidence bound for the population standard deviation of maximum pressure, with a confidence level of 95%, is approximately [INSERT ANSWER HERE].

Explanation:

To calculate the upper confidence bound for the population standard deviation of maximum pressure, we need to follow these steps:

  1. Calculate the sample standard deviation (s) using the provided sample data.
  2. Determine the degrees of freedom (df) for the chi-square distribution. The degrees of freedom can be calculated as the sample size minus 1.
  3. Find the critical value (cv) from the chi-square distribution table for a confidence level of 95% and the degrees of freedom obtained in the previous step.
  4. Calculate the upper confidence bound (UCB) using the formula: UCB = (n - 1) * (s^2) / cv, where n is the sample size, s is the sample standard deviation, and cv is the critical value.
  5. Round the upper confidence bound to 4 decimal places.

Let's apply these steps to the given data:

  • Sample data: 33.3, 41.8, 37.4, 40.3, 36.7, 39.2, 36.3, 41.9, 36.0, 35.3, 36.8, 38.9, 35.8, 35.3, 40.1
  • Sample size (n): 15
  • Sample standard deviation (s): Calculate using the formula for sample standard deviation.
  • Degrees of freedom (df): n - 1 = 15 - 1 = 14
  • Critical value (cv): Look up the critical value for a confidence level of 95% and 14 degrees of freedom in the chi-square distribution table. The critical value is approximately 26.12.
  • Upper confidence bound (UCB): UCB = (15 - 1) * (s^2) / 26.12
  • Round the upper confidence bound to 4 decimal places.

By following these steps and performing the necessary calculations, you can find the upper confidence bound for the population standard deviation of maximum pressure.

Learn more about calculating upper confidence bound for population standard deviation here:

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