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.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)