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Answer:
Confidence interval : to
Step-by-step explanation:
A quality analyst selects twenty racquets and obtains the following lengths:
21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24
So, sample size = n =20
Now we are supposed to find Construct a 99.9% confidence interval for the mean length of all the junior's tennis racquets manufactured at this plant.
Since n < 30
So we will use t-distribution
Confidence level = 99.9%
Significance level = α = 0.001
Now calculate the sample mean
X=21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24
Sample mean =
Sample mean =
Sample mean =
Sample standard deviation =
Sample standard deviation =
Sample standard deviation= s =
Degree of freedom = n-1 = 20-1 -19
Critical value of t using the t-distribution table = 3.883
Formula of confidence interval :
Substitute the values in the formula
Confidence interval :
Confidence interval : to
Confidence interval : to
Hence Confidence interval : to