91Ó°ÊÓ

As the number of degrees of freedom in the \(t\) -distribution increases, the spread of the distribution ________ (increases/decreases).

True or False: The chi-square distribution is symmetric.

True or False: The shape of the chi-square distribution depends on its degrees of freedom.

True or False: A \(95 \%\) confidence interval for a population proportion with lower bound 0.45 and upper bound 0.51 means there is a \(95 \%\) probability the population proportion is between 0.45 and 0.51

True or False: To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.

As the sample size used to obtain a confidence interval increases, the margin of error _______ (increases/decreases).

Find the critical values \(\chi_{1-\alpha / 2}^{2}\) and \(\chi_{\alpha / 2}^{2}\) for the given level of confidence and sample size. \(98 \%\) confidence, \(n=23\)

(a) Find the \(t\) -value such that the area in the right tail is 0.10 with 25 degrees of freedom. (b) Find the \(t\) -value such that the area in the right tail is 0.05 with 30 degrees of freedom. (c) Find the \(t\) -value such that the area left of the \(t\) -value is 0.01 with 18 degrees of freedom. [Hint: Use symmetry.] (d) Find the critical \(t\) -value that corresponds to \(90 \%\) confidence. Assume 20 degrees of freedom.

Determine the critical value \(z_{\alpha / 2}\) that corresponds to the given level of confidence. \(99 \%\)

(a) Find the \(t\) -value such that the area in the right tail is 0.02 with 19 degrees of freedom. (b) Find the \(t\) -value such that the area in the right tail is 0.10 with 32 degrees of freedom. (c) Find the \(t\) -value such that the area left of the \(t\) -value is 0.05 with 6 degrees of freedom. [Hint: Use symmetry.] (d) Find the critical \(t\) -value that corresponds to \(95 \%\) confidence. Assume 16 degrees of freedom.