91影视

Based on Data set 4 鈥淏irth鈥� in Appendix B,the summary statistics for randomly selected weights of newborn girls as,\({\rm{n}}\,{\rm{ = }}\,{\rm{205}}\),\(\bar x\, = 30.4\,{\rm{hg}}\),\(s\, = 7.1\,{\rm{hg}}\)

And, the confidence level is 95%.

The critical value is the border value which separates the sample statistics that are significantly high or low from those sample statistics that are not significant.

For randomly selected samples, the conditions for t-distribution and normal distribution are as follow,

If\(\sigma \)is not known and\({\rm{n}} > 30\)then t-distribution is suitable to find the confidence interval.

If\(\sigma \)is known and\({\rm{n}} > 30\)then normal distribution is suitable to find the confidence interval.

In this case,\(\sigma \)is unknown and\({\rm{n}} = 61\), where n>30.So, t-distribution applies here.

.

To find the critical value\({t_{\frac{\alpha }{2}}}\), it requires a value for the degrees of freedom.

The degree of freedom is,

\(\)

\(\begin{array}{c}{\rm{degree}}\,\,\,{\rm{of}}\,\,\,{\rm{freedom}}\,\,\, = n - 1\\ = 205 - 1\\ = 204\end{array}\)

The 95% confidence level corresponds to\(\alpha = 0.05\), so there is an area of 0.025 in each of the two tails of the t-distribution.

Referring to Table A-3 critical value of t-distribution, the critical value is expressed as,

\(\begin{array}{c}{t_{\frac{\alpha }{2}}} = {t_{\frac{{0.05}}{2}}}\\ = {t_{0.025}}\end{array}\)

It is obtained from the intersection of column with 0.05 for the 鈥淎rea in Two Tails鈥� (or use the same column with 0.025 for the 鈥淎rea in One Tail鈥�) and the row value number of degrees of freedom is 204, which is 1.972.