Question

Suppose we want to calculate a 94% confidence interval for a sample mean with a sample size n=54. We ignore the variance of the variable in the population. What is the numerical value corresponding to the order quantile used in calculating the confidence interval? Show your approach

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Tiffany

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96 Answers

1. Determine the confidence level: 94%.

2. Calculate the significance level: \alpha = 1 - 0.94 = 0.06 .

3. Divide the significance level by 2 to find the tail probability: \alpha/2 = 0.03 .

4. The degrees of freedom for our sample is n - 1 = 54 - 1 = 53 .

5. Look up the value in the t-distribution table corresponding to 53 degrees of freedom and a two-tailed probability of 0.06. Alternatively, you can use statistical software or a calculator.

The t-score that corresponds to a cumulative probability near (1 - 0.03) for 53 degrees of freedom is approximately1.922 .

Thus, the numerical value is1.922 .

2. Calculate the significance level:

3. Divide the significance level by 2 to find the tail probability:

4. The degrees of freedom for our sample is

5. Look up the value in the t-distribution table corresponding to 53 degrees of freedom and a two-tailed probability of 0.06. Alternatively, you can use statistical software or a calculator.

The t-score that corresponds to a cumulative probability near (1 - 0.03) for 53 degrees of freedom is approximately

Thus, the numerical value is

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