A sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.77 mpa.

For this problem, the confidence interval is the one we are looking for. Since the confidence level is not given, we assume that it is 95%.

The formula for the confidence interval is: mean ± t (α/2) (n-1) * s √1 + 1/n

Where:

α = 5%

α/2 = 2.5%

t 0.025, 19 = 2.093 (check t table)

n = 20

df = n - 1 = 20 - 1 = 19

So plugging in our values:

8.41 ± 2.093 * 0.77 √ 1 + 1/20

= 8.41 ± 2.093 * 0.77 (1.0247)

= 8.41 ± 2.093 * 0.789019

= 8.41 ± 1.65141676

= 6.7586 < x < 10.0614