Sample of 15 test-tubes tested for number of times they cracked gave the sample mean of 1230 with a standard deviation of 270. Construct 99% confidence interval mean time a test tube can be cracked, give the lower limit of the interval. Assume normality.

Answer 1

To construct a 99% confidence interval for the mean time a test tube can be cracked, we will use the formula:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / sqrt(sample size))

First, we need to find the critical value corresponding to a 99% confidence level. Since the sample size is less than 30, we will use a t-distribution instead of a z-distribution.

The degrees of freedom for a t-distribution with 15 test tubes is 15 - 1 = 14.

Using a t-table or calculator, we find that the critical value for a 99% confidence level and 14 degrees of freedom is approximately 2.977.

Now, we can calculate the confidence interval:

Confidence Interval = 1230 ± (2.977) * (270 / sqrt(15))

Confidence Interval = 1230 ± 222.047

Lower Limit = 1230 - 222.047 = 1007.953

The lower limit of the 99% confidence interval for the mean time a test tube can be cracked is approximately 1007.953.