Answer:
With 95% confidence, estimate loaded mass at which the additional truss will fail falls between 1.4258 and 1.5742 kg. Because the masses are used in 50g increments, our interval is between 1.45 and 1.60 kg
Step-by-step explanation:
Seven loads of failure are measured. Let S be the sample of these values, then
S={1.40, 1.40, 1.45, 1.50, 1.55, 1.60, 1.60}
Size of the sample, N=7
Mean of the sample, M=1.50
Standard Deviation of the sample, s =0.0802
To estimate the loaded mass at which the additional truss will fail with 95% confidence, we need to calculate the margin of error for the sample mean.
Confidence interval for the estimate would be
M±
where M is the mean of the sample, t is the appropriate t-value for 95% level of confidence, s is the sample standard deviation and N is the sample size.
Since our sample is small (<30), we'll use corresponding t-table value for <em>95% confidence</em> level and <em>6 (M-1) degrees of freedom</em>, which is 2.447
Our formula becomes 1.50±
i.e 1.50±0.0742
Therefore estimate loaded mass at which the additional truss will fail falls between 1.4258 and 1.5742 kg. Because the masses are used in 50g increments, our interval is between 1.45 and 1.60 kg