A study of 60 bolts of carpet showed that their average length was 180 yards. The standard deviation of the population is 6 yards. Which of the following is the 99% confidence interval for the mean length per bolt of carpet?
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99% = mean ± 2.575 SEm
SEm = SD/√n
You do the math.
To find the 99% confidence interval for the mean length per bolt of carpet, we can use the formula:
Confidence interval = sample mean +/- (critical value * standard deviation / square root of sample size)
First, let's determine the critical value. Since we have a sample size of 60 and want a 99% confidence level, we will use a z-score.
The critical value for a 99% confidence level can be found using a standard normal distribution table or a calculator. In this case, the critical value is approximately 2.61.
Next, we plug the values into the formula:
Confidence interval = 180 +/- (2.61 * 6 / √60)
Calculating this expression, we get:
Confidence interval = 180 +/- (15.66 / 7.75)
Simplifying the expression, we get:
Confidence interval = 180 +/- 2.02
Therefore, the 99% confidence interval for the mean length per bolt of carpet is approximately (177.98, 182.02) yards.
To find the 99% confidence interval for the mean length per bolt of carpet, we can use the formula:
Confidence Interval = Mean ± (Z-score * Standard Deviation / √n)
Where:
- Mean is the average length of the bolts of carpet (180 yards).
- Z-score is the critical value corresponding to the desired confidence level. For a 99% confidence level, the critical value is 2.576.
- Standard Deviation is the standard deviation of the population (6 yards).
- n is the sample size (60 bolts of carpet).
Substituting the values into the formula, we get:
Confidence Interval = 180 ± (2.576 * 6 / √60)
Calculating the expression inside the parentheses:
2.576 * 6 = 15.456
Calculating the square root of the sample size:
√60 ≈ 7.746
Now, divide the expression by the square root of the sample size:
15.456 / 7.746 ≈ 1.994
The confidence interval is therefore:
180 ± 1.994
To calculate the upper and lower bounds of the confidence interval, we add and subtract 1.994 from the mean:
Lower bound: 180 - 1.994 ≈ 178.006
Upper bound: 180 + 1.994 ≈ 181.994
Therefore, the 99% confidence interval for the mean length per bolt of carpet is approximately 178.006 to 181.994 yards.