Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the level of significance with degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the level of significance based on a sample size of n. (c) Determine the critical value(s) for a two-tailed test of a population mean at the level of significance based on a sample size of n.

(a) The critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.

(b) The critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.

(c) The critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.

Step-by-step explanation:

We have to find the critical t values for each of the following levels of significance and sample sizes given below.

As we know that in the t table there are two columns. The horizontal column is represented by the symbol P which represents the level of significance and the vertical column is represented by the symbol '' which represents the degrees of freedom.

(a) A right-tailed test of a population mean at the α=0.01 level of significance with 15 degrees of freedom.

So, here the level of significance = 0.01

And the degrees of freedom = n - 1  = 15

Now, in the t table, the critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.

(b) A left-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 20.

So, here the level of significance = 0.05

And the degrees of freedom = n - 1  

                                                = 20 - 1 = 19

Now, in the t table, the critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.

(c) A two-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 13.

So, here the level of significance = = 0.025 {for the two-tailed test}

And the degrees of freedom = n - 1  

                                                = 13 - 1 = 12

Now, in the t table, the critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.

b

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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