Question 4.15: What is the 95% confidence interval for the data in Table 4....

The mean and standard deviation for this sample are, respectively, 3.117 \mathrm{~g} and 0.051 \mathrm{~g}. Since the sample consists of seven measurements, there are six degrees of freedom. The value of t from Table 4.14, is 2.45. Substituting into equation 4.13 gives

\mu=\bar{X} \pm \frac{t s}{\sqrt{n}}=3.117 \pm \frac{(2.45)(0.051)}{\sqrt{7}}=3.117 \pm 0.047 \mathrm{~g}

Thus, there is a 95 \% probability that the population’s mean is between 3.070 and 3.164 \mathrm{~g}.