a simple random smaple of 55 mathematics teachers were timed as they completed sudoku puzzles. Their mean completion time was 20.3 minutes. The population standard deviation is assumed to be 12 mintues and times vary normally. Find 99% confidence interval for the mean time for completing a sudoku puzzle by a math teacher.
99% = mean ± 2.575 SEm (Standard Error of the mean)
SEm = SD/√(n-1)
You can do the calculations.
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To find the 99% confidence interval for the mean time for completing a sudoku puzzle by a math teacher, we can use the formula:
Confidence Interval = sample mean ± (critical value * standard deviation / √n)
First, let's calculate the critical value. Since we want a 99% confidence interval, we need to find the z-score corresponding to a 99% confidence level. This means we want to find the z-score that leaves 1% in the tails, which is split evenly between both tails.
The z-score for a 99% confidence level with a two-tailed test can be found using a z-score table or a calculator. The z-score that corresponds to a one-tailed confidence level of 0.995 is approximately 2.576.
Next, we'll substitute the given values into the formula:
- sample mean (x̄) = 20.3 minutes
- standard deviation (σ) = 12 minutes
- sample size (n) = 55
- critical value (z) = 2.576
Confidence Interval = 20.3 ± (2.576 * 12 / √55)
Now, we can calculate the confidence interval by substituting the values and evaluating the expression:
Confidence Interval = 20.3 ± (2.576 * 12 / √55)
= 20.3 ± (2.576 * 12 / 7.416)
= 20.3 ± 4.218
The lower bound of the confidence interval is 20.3 - 4.218 = 16.082 minutes.
The upper bound of the confidence interval is 20.3 + 4.218 = 24.518 minutes.
Therefore, the 99% confidence interval for the mean time for completing a sudoku puzzle by a math teacher is approximately (16.082, 24.518) minutes.