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Complete Question

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 40 girls and 40 boys in a community and gave them the standard memory test. The mean score for girls was 68 and the standard deviation of mean was 5.0. The mean score for boys was 66 and the standard deviation of mean was 5.0. What is the p-value and your conclusion at alpha 0.05

Answer:

The p-value is  [tex]p-value =0.073614[/tex]

 The conclusion is  

There is sufficient evidence to support the claim  that there was no significant difference between boys and girls on a standard memory test

Step-by-step explanation:

From the question we are told that

      The sample size of boys and girls is  [tex]n_1= n_2 = n = 40[/tex]

      The standard deviation is  [tex]s_1= s_2 = s = 5[/tex]

        The level of significance is  [tex]\alpha = 0.05[/tex]

       The sample mean for boys is  [tex]\= x_1 =66[/tex]  

The null hypothesis is  [tex]H_o : \mu_1 = \mu_2[/tex]

The alternative hypothesis is  [tex]H_a : \mu_1 < \mu_2[/tex]

 Generally the test statistics is mathematically represented as

           [tex]z = \frac{\= x_1 - \= x_2 }{ \sqrt{\frac{s_1 ^2 }{n_1} + \frac{s_2 ^2 }{n_1} } }[/tex]

=>       [tex]z = \frac{66 -68 }{ \sqrt{\frac{5^2 }{40} + \frac{5 ^2 }{40} } }[/tex]

=>       [tex]z = -1.789[/tex]

From the z table  the area under the normal curve to the left corresponding to    -1,789   is

          [tex]P(Z < -.1789 ) = 0.036807[/tex]

Generally the p-value is mathematically represented as

         [tex]p-value = 2 P(Z < -.1789 )[/tex]

=>      [tex]p-value = 2 * 0.036807[/tex]

=>      [tex]p-value =0.073614[/tex]

From the values obtained we see that  [tex]p-value < \alpha[/tex] hence

The decision rule is  

Fail to reject the null hypothesis

 The conclusion is  

There is sufficient evidence to support the claim  that there was no significant difference between boys and girls on a standard memory test

Answer:

12(1+3)

Step-by-step explanation:

gcf: 12

12/12=1

36/12=3

Answer:

The answer to this question is: (B)

Which is "14"

Step-by-step explanation:

Substitute the value of the variable into the equation and simplify.

HOPE this helped if so PLEASE leave a "Rating" and a "LIke" and PLEASE mark me brainliest if I have the best answer! THANKS! :))))

Answer:

2x + 4

To model 2x+4, you need :

2 positive x-tiles to represent 2x.

4 positive unit tiles to represent 4.

3x+(-1)

To model 3x+(-1), you need :

3 positive x-tiles to represent 3x.

1 negative unit tile to represent (-1).

if its wrong sorry u can report me

Answer:

The answer is 6. Hope this helped :D

Answer:

674,800

Step-by-step explanation:

Answer:

674,800

Step-by-step explanation:

I did the unit test on edge 2021

Answer:

It is a relflection.This is a reflection horizontally bc they are not dialatedor rotated. please vote brainliest

Step-by-step explanation:

Answer:

I don't get it the two triangles look the same

Step-by-step explanation:

Answer:

The domain is the set of all the values of x, so it would be -3, -5, -6, -9, 0. The range would be every set of y, so it would be 7, -8, -1, -3. Finally, this relation is indeed a function.

Domain: -3, -5, -6, -9, 0

Range: 7, -8, -1, -3

Is it a function? Yes

Answer:3.5

Step-by-step explanation:

All Uu have to do is JuSs divide .

Answer:

the answer is x over -2 × 14

Answer:-2,2 -7,7 -14,14 0,0

Step-by-step explanation:im not really good at this but i tried and i oped it worked

Answer:

If Clara gets 4 people in 10 phone calls, then she will obviously get 16 people, because there are 40 calls, with 4 people each 10 calls. Meanwhile, with Toby getting 3:8, he will get 15 people in total. 3:8 is equal to 15:40. Clara will have more people in 40 phone calls

Step-by-step explanation:

Answer: If a car travels 55 miles per hour for 2 hours it will be 110 hour I guess

Step-by-step explanation: I think you want help here um I’m in 7th grade I don’t think I like this before but I can try to answer it, Is this h-help you

Answer: about 500

Step-by-step explanation:

Answer:

Step-by-step explanation:

800 meters

Answer:

Total assets: 110,000

Total liabilities: 70,000

Step-by-step explanation:

Step-by-step explanation:

0.345454...... = 4311/9900

0.5888..... = 530/900

0.68080..... = 674/990

4.98585..... = 4936/990

8.18080...... = 8099/990

Answer:

y = 1.75

x = 1.25

Step-by-step explanation:

Since the triangles have equal angles, you can use ratios to solve for x and y.

For y:

[tex]\frac{8}{10} =\frac{7}{a} \\8a=70\\a=8.75[/tex]

Subtract 7 from a to find y.

y = 8.75 - 7

y = 1.75

For x:

[tex]\frac{8}{10} =\frac{5}{b} \\8b=50\\b=6.25[/tex]

Subtract 5 from b to find x.

x = 6.25 - 5

x = 1.25

Step-by-step explanation:

Using Difference of Squares,

16y⁴ - 256x¹²

= 16(y⁴ - 16x¹²)

= 16(y² + 4x⁶)(y² - 4x⁶)

= 16(y² + 4x⁶)(y + 2x³)(y - 2x³).

Step-by-step explanation:

Answer:

the time period is 9 years

Step-by-step explanation:

The computation of the number of years is as follows:

As we know that

Future value = Present value × (1 + rate of interest)^number of years

$49,000 = $38,000 × (1 + 0.03)^number of years  

$49,000 ÷ $38,000 = 1.03^number of years  

tlog(1.03) = log($49 ÷ $38)

Now apply the log formula in calculator or in excel  

t = log(49 ÷ 38) / log(1.03)

= 8.6

= 9 years

Hence, the time period is 9 years

Answer:

[tex]A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right][/tex]

Step-by-step explanation:

Given

[tex]T:R^3->R^2[/tex]

[tex]T(e_1) = (1,2)[/tex]

[tex]T(e_2) = (-4,6)[/tex]

[tex]T(e_3) = (2,-6)[/tex]

Required

Find the standard matrix

The standard matrix (A) is given by

[tex]Ax = T(x)[/tex]

Where

[tex]T(x) = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right][/tex]

[tex]Ax = T(x)[/tex] becomes

[tex]Ax = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right][/tex]

The x on both sides cancel out; and, we're left with:

[tex]A = [T(e_1)\ T(e_2)\ T(e_3)][/tex]

Recall that:

[tex]T(e_1) = (1,2)[/tex]

[tex]T(e_2) = (-4,6)[/tex]

[tex]T(e_3) = (2,-6)[/tex]

In matrix:

[tex](a,b)[/tex] is represented as: [tex]\left[\begin{array}{c}a\\b\end{array}\right][/tex]

So:

[tex]T(e_1) = (1,2) = \left[\begin{array}{c}1\\2\end{array}\right][/tex]

[tex]T(e_2) = (-4,6)=\left[\begin{array}{c}-4\\6\end{array}\right][/tex]

[tex]T(e_3) = (2,-6)=\left[\begin{array}{c}2\\-6\end{array}\right][/tex]

Substitute the above expressions in [tex]A = [T(e_1)\ T(e_2)\ T(e_3)][/tex]

[tex]A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right][/tex]

Hence, the standard of the matrix A is:

[tex]A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right][/tex]

Answer:

9/2 is the slope of the graphed line.

The second statement is true.

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

Answer:  Approximately 1.9 atm

============================================

Work Shown:

[tex]P_1*V_1 = P_2*V_2 \ \text{ ... Boyle's Law}\\\\4.5*1.5 = P_2*3.5\\\\6.75 = P_2*3.5\\\\P_2*3.5 = 6.75\\\\P_2 = \frac{6.75}{3.5}\\\\P_2 \approx 1.92857142857142\\\\P_2 \approx 1.9\\\\[/tex]

If the volume is 3.5 liters, then the pressure is approximately 1.9 atm.

Note the increase in volume leads to the reduction of pressure, and vice versa. The two variables have an inverse relationship.

-----------

As a check,

[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.9*3.5\\\\6.75 \approx 6.65\\\\[/tex]

We don't get the exact thing on both sides, but the two sides are close enough. We have rounding error due to P2 being not exact.

A more accurate check could be

[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.92857*3.5\\\\6.75 \approx 6.749995\\\\[/tex]

which has the two sides much closer to one another. This helps us verify the answer.

Answer:

$16

Step-by-step explanation:

If he saves $8 for every $14, he earned $28, which is twice the $14, he will save twice the $8 or $16.

Answer:

50 degrees

Step-by-step explanation:

40+50=130

130-180

50

Answer:

50

I have not done this in years!

Answer:

129024.387

Step-by-step explanation:

16e^(-0.000121)*8065 = 129024.387

Answer:

Step-by-step explanation:

y=−3x+12

when x=0 then y=12 , the y intercept is (0,12)

when y=0 then -3x+12=0, -3x=-12, x=12/3=4

x intercept =(4,0)

Answer:

Ok thats really cool thanks :)

Answer:

he has 11 dimes and 15 nickels

Step-by-step explanation:

i kept going down reducing the amount of dimes and adding to the amount of nickels and found that 11 dimes is $1.10 and 15 nickels is $0.75