The test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

<h3>What are null hypotheses and alternative hypotheses?</h3>

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics course.

Then they are given a post-test once the professor has concluded lecturing on the material.

Pre-test and post-test scores for 4 students in an elementary statistics class are given below.

Then we have

$\mu _d = \mu _{post} - \mu _{pre}$

Then the null hypotheses and alternative hypotheses will be

H₀: $\mu _d = 0$

Hₐ: $\mu _d > 0$

Then the test statistic will be

$\rm \overline{x} _d = \dfrac{\Sigma x_d}{n} = \dfrac{15+12+10+1}{4}\\\\\overline{x} _d = 9.5$

Then

$\rm S_d = 6.02$

The test statistic value is given by

$\rm t = \dfrac{\overline{x} _d }{\dfrac{S_d}{\sqrtn}} \\\\t = \dfrac{9.5}{\dfrac{6.02}{\sqrt4}}\\\\t = 3.16$

Since this is a right-tailed test, so the critical value is given by

$\rm t_{n-1}(\alpha ) = t_3 (0.05) = 2.353$

Since the test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

Hence, we can conclude that $\mu _d > 0$ that is test scores have improved.

More about the null hypotheses and alternative hypotheses link is given below.

brainly.com/question/9504281

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7 0

2 years ago

She bought 9 cases of tile for $189. She realizes she bought too much tile and returns 4 unopened cases to the store.

nadya68 [22]

So the 1 case of tile is $21
$21 x 5 = $105

8 0

4 years ago

AB is dilated by a scale factor of 3 to form AB . Point O is the center of dilation, and point O lies on AB . If the slope of AB

avanturin [10]

<h2>Answer:</h2>

Option: D is the correct answer.

D. The slope of is 3, and passes through O.

<h2>Step-by-step explanation:</h2>

It is given that:

AB is dilated by a scale factor of 3 to form AB .

Also, the line AB pass through the origin.

So, if AB pass through (0,0) and some point (x,y) then the slope of line AB is:

$Slope=\dfrac{y-0}{x-0}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3$

( Since, it is given the slope of AB is 3 )

Now , if AB is dilated to A'B' by a scale factor of 3 then

(0,0) → (0,0)

and

(x,y) → (3x,3y)

i.e. (0,0) and (3x,3y) will lie on A'B'.

Hence, the slope of line A'B' is given by:

$Slope=\dfrac{3y-0}{3x-0}\\\\i.e.\\\\Slope=\dfrac{3y}{3x}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3$

Hence, both have the same slope.

The answer is : Option: D

5 0

4 years ago

On a family trip, natalie counted 3 groups of 5 motocycles and additonal 7 solo motocycles. write an expression for the number o

timama [110]

3×5=× would be the answer

4 0

3 years ago

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