The article "influence of penetration rate on penetrometer resistance" (see textbook for reference) presents measures of penetration resistance for a certain fine-grained soil. fifteen measurements, expressed as a multiple of a standard quantity, had a mean of 2.64 and a standard deviation of 1.02. find a 95% of confidence interval for the mean penetration resistance for this soil.

The 95% of confidence interval for the mean penetration resistance for this soil is (2.0823, 3.1977).

Step-by-step explanation:

The sample size is 15.

The first step to solve this problem is finding how many degrees of freedom there are, that is, the sample size subtracted by 1. So

Then, we need to subtract one by the confidence level and divide by 2. So:

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 14 and 0.025 in the t-distribution table, we have .

Now, we need to find the standard deviation of the sample. That is:

Now, we multiply T and s

For the lower end of the interval, we subtract the mean by M. So 2.64 - 0.5577 = 2.0823

For the upper end of the interval, we add the mean to M. So 2.64 + 0.5577 = 3.1977

The 95% of confidence interval for the mean penetration resistance for this soil is (2.0823, 3.1977).

college