Imagine that a researcher appropriately conducts a two-tailed, independent-samples t test with an alpha level of 0.05 (5%). The first group has degrees of freedom equal to 19. The second group has degrees of freedom equal to 21. What is the critical value (as a t statistic) that would cut off the upper 2.5% of the corresponding sampling distribution. Please provide three decimal places when reporting your answer.

For the first group, with 19 degrees of freedom, the critical value is t=2.093.

For the second group, with 21 degrees of freedom, the critical value is t=2.080.

Step-by-step explanation:

The critical value of the t-statistic depends on the significance level and the degrees of freedom of the sample.

For a significance level of 0.05, for a two-tailed test, there is an upper 2.5% and a lower 2.5%.

For the first group, with 19 degrees of freedom, the critical value is t=2.093.

For the second group, with 21 degrees of freedom, the critical value is t=2.080.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have