You are researching a new catalyst to assist in the workability (ease of handlin

Question

You are researching a new catalyst to assist in the workability (ease of handling) of cast-in-place concrete. To work properly, the catalyst must dissolve quickly in the presence of Portland cement and water. Twenty four (24) independent tests were made which resulted in a mean dissolution time of 72 seconds and a sample standard deviation of 5 seconds. Using a Student's t distribution (assume a two sided interval): a. Find the 80% confidence intervals for the mean dissolution time. b. Find the 90% confidence intervals for the mean dissolution time. c. Find the confidence level for [69.89, 74.11] 1.

Explanation / Answer

We can find the 80% confidence interval by these steps:-
Step 1: Subtracting 1 from our sample size. 24 – 1 = 23. This gives us degrees of freedom.

Step 2: Subtracting the confidence level from 1, then dividing by two we get
(1 – 0.80) / 2 = 0.10

Step 3: Lookin up to our answers to step 1 and 2 in the t-distribution table. For 23 degrees of freedom (df) and = 0.10, our result is 1.319.

Step 4: Divide your sample standard deviation by the square root of your sample size.
5 / (24) = 1.020620

Step 5: Multiply step 3 by step 4.
1.020620 × 1.319 = 1.346198

Step 6: For the lower end of the range, subtract step 5 from the sample mean.
72 – 1.346 = 70.654

Step 7: For the upper end of the range, add step 5 to the sample mean.
72 + 1.346 = 73.346

That's how we can calculate the confidence interval.

Similarly for a confidence interval of 90 we have to replace 0.80 with 0.90 and check value in T-distribution table everything else will be same.

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