A shirt is on sale for 20% off. Sandy paid $8 for the shirt. What was the shirt's regular price?

Answer:

$215,892.50

Step-by-step explanation:

This is a problem of compound interest.

In compound interest Amount A for principal p charged at interest r% per annum is given by

A = p(1+r/100)^n

where n is the time period in years.

_____________________________

given

p = $100,000

r = 8%

t = 10 years

A= 100,000( 1+ 8/100)^10

A= 100,000( 1.08)^10

A = $215,892.50

So , you need to pay $215,892.50 in total to debt cleared of debt.

Answer:

In the error term.

Step-by-step explanation:

A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).

Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.

Answer:

a

See in the explanation

a-2.

Discrete

b-1.

Mean = 4.201

Standard Deviation = 2.069

b-2.

4.201

c.

Mean = 16.153

Standard Deviation = 8.079

Step-by-step explanation:

Given Data:

Number of Hours         Frequency               Amount Charged  

          1                                 16                                $3        

          2                                34                                 6  

          3                                51                                  12  

          4                                39                                 16  

          5                                34                                 21

          6                                 16                                 24

          7                                  9                                  27

          8                                 30                                 29

                                       ∑f = 229

a. Convert the information on the number of hours parked to a probability distribution:

The probability is calculated by dividing each frequency by 229. For example probability of Hour 1 is calculated as:

16 / 229 = 0.06987

This way all the hours probabilities are computed. The probability distribution is given below

Hours          Probability

   1                0.06987

   2               0.14847

   3               0.2227

   4               0.1703

   5               0.1485

   6               0.0699

   7               0.0393

   8               0.1310

   ∑                    1

a-2. Is this a discrete or a continuous probability distribution?

This is a discrete probability distribution as the probability of each hour of between 0 and​ 1 and the sum of all the probabilities of hours is 1.

b-1. Find the mean and the standard deviation of the number of hours parked.

First multiply each value of Number of hours by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:

Number of Hours Parked

fx

16

68

153

156

170

96

63

240

Now add the above computed products.

∑fx = 16+68+153+156+170+96+63+240  = 962

Compute Mean:

Now the formula to calculate mean:

Mean = Sum of the value / Number of value

         = ∑fx / ∑f

         = 962 / 229

Mean = 4.201

Compute Standard Deviation:

Let x be the Number of hours.        

Let f be the frequency

First calculate (x-x_bar) where x is each number of hours and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 4.201

For example for the Hour = 1 , and mean = 4.201

Then (x-[tex]\frac{}{x}[/tex]) = 1 - 4.201 = -3.201

So calculating this for every number of hour we get:

(x-[tex]\frac{}{x}[/tex])

-3.201

-2.201

-1.201

-0.201

0.799

1.799

2.799

3.799

Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])

For example the first entry of below calculation is computed by:

 (x-[tex]\frac{}{x}[/tex])² = (-3.201 )² = 10.246401

  (x-[tex]\frac{}{x}[/tex])²

10.246401

4.844401

1.442401

0.040401

0.638401

3.236401

7.834401

14.432401

Next multiply each entry of  (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:

(x-[tex]\frac{}{x}[/tex])² * f = 10.246401  * 16 = 163.942416

(x-[tex]\frac{}{x}[/tex])² * f

163.942416

164.709634

73.562451

1.575639

21.705634

51.782416

70.509609

432.97203

Now the formula to calculate standard deviation is:

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

Here

n = ∑f = 229

∑(x-[tex]\frac{}{x}[/tex])² * f  is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f

∑(x-[tex]\frac{}{x}[/tex])² * f = 980.759829

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

  = √980.759829  /  229

  = √4.2827940131004

  = 2.0694912449924

S = 2.069

b-2) How long is a typical customer parked?

That is the value of mean calculated in part b-1. Hence

Typical Customer Parked for 4.201 hours

c) Find the mean and the standard deviation of the amount charged.

First multiply each value of Amount Charged by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:

fx

48

204

612

624

714

384

243

870

Now add the above computed products.

∑fx = 48+204+612+624+714+384+243+870  = 3699

Compute Mean:

Now the formula to calculate mean:

Mean = Sum of the value / Number of value

         = ∑fx / ∑f

         = 3699 / 229

Mean = 16.153

Compute Standard Deviation:

Let x be the Amount Charged.        

Let f be the frequency.

First calculate (x-x_bar) where x is each value of Amount charged and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 16.153

For example for the Amount Charged = 3 , and mean = 16.153

Then (x-[tex]\frac{}{x}[/tex]) = 3 - 16.153 = -13.153

So calculating this for every number of hour we get:

(x-[tex]\frac{}{x}[/tex])

-13.153

-10.153

-4.153

-0.153

4.847

7.847

10.847

12.847

Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])

For example the first entry of below calculation is computed by:

 (x-[tex]\frac{}{x}[/tex])² = (-13.153  )² = 173.001409

  (x-[tex]\frac{}{x}[/tex])²

173.001409

103.083409

17.247409

0.023409

23.493409

61.575409

117.657409

165.045409

Next multiply each entry of  (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:

(x-[tex]\frac{}{x}[/tex])² * f = 173.001409  * 16 =  

   (x-[tex]\frac{}{x}[/tex])² * f

2768.022544

3504.835906

879.617859

0.912951

798.775906

985.206544

1058.916681

4951.36227

∑(x-[tex]\frac{}{x}[/tex])² = 14947.65066

Now the formula to calculate standard deviation is:

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

Here

n = ∑f = 229

∑(x-[tex]\frac{}{x}[/tex])² * f  is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f

∑(x-[tex]\frac{}{x}[/tex])² * f = 14947.65066

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/ ∑f

  = √65.273583668122

  = 8.0792068712295

S = 8.079

Answer:

B. More

Step-by-step explanation:

This is according to the law of large numbers

An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.

Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.

An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed

Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.

Learn more about probability here:

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Answer:

yes

Step-by-step explanation:

yes E

Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.

The value of the y-intercept is 9.

Step-by-step explanation:

Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]

[tex]=\dfrac{8}{2}=4[/tex]

So, the slope of the line that passes through (2, 12) and (4, 20) is 4.

To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).

[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]

By comparison,  c= 9

Hence, the value of the y-intercept is 9.

Answer:

2 servings of salad and 1 serving of soup

Step-by-step explanation:

In the given scenario the aim is to minimise the fat content of the food combination.

Fat content of soup is 3mg while fat content of salad is 2 mg.

Using Soup as 0 and Salad as 2 will not give the required vitamin content

The logical step will be to keep servings of soup to the minimum.

Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1

1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.

This will not work because amount of vitamin B complex is not up to 10 mg

2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat

This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.

Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving

Answer: C

Step-by-step explanation:

Since this is an isosceles triangle as indicated by the markers on QP and PR, we know that QS and SR are equivalent.

To find the value of n, we set QS and SR equal to each other.

6n+3=4n+11                     [combine like terms]

2n=8                                 [divide both sides by 2]

n=4

Now that we know n=4, we know that A is incorrect. What we can do is use the value of n to solve for QS, SR, and QR.

QS

6(4)+3=13

Since the length of QS is 13, we know B is incorrect.

SR

4(4)+11=27

Since SR is 27, C is a correct answer.

QR

13+27=40

Since QR is 40, the only correct answer is C.

Answer:

Student is ready for college level mathematics.

The null hypothesis will be H0 = 25

The alternative hypothesis is Ha > 25

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to  test a hypothesis.

Answer:

First option

Step-by-step explanation:

Common ratio is greater than 1

Answer:

Step-by-step explanation:

Given x = 5, y = 3/4 and z = -1/7, 2=we are to calculate [tex]\frac{xz}{y}[/tex]. Substituting the value of x, y and z into the expression will give;

[tex]= \frac{xz}{y}\\\\ \frac{5(-1/7)}{3/4} \\= \frac{-5/7}{3/4}\\\\= \frac{-5}{7} * \frac{4}{3}\\ \\ = \dfrac{-20}{21}\\[/tex]

Hence the value of the expression is -20/21

[tex]\text{Solve the systems of equations:}\\\\2y+7x=-5\\5y-7x=12\\\\\text{Solve by adding and subtracting}\\\\7y=7\\\\\text{Divide}\\\\y=1\\\\\text{To find x, plug 1 into y in one of the equations and solve:}\\\\2(1)+7x=-5\\\\2+7x=-5\\\\\text{Subtract 2 from both sides}\\\\7x=-7\\\\\text{Divide by 7}\\\\x=-1\\\\\boxed{y=1\,\,and\,\,x=-1}[/tex]

Answer:

Step-by-step explanation:

To solve the question we use the following conversion

1 feet per second = 1.09728 kilometers per hour

Therefore 11 ,000 feet per second is

[tex]11000 \times 1.09728[/tex]

We have the final answer as

Hope this helps you

Answer:

This is a binomial experiment .

Step-by-step explanation:

As the percent is not indicated the success is the amount of percent (if given) say it is 10 % . So p will be equal to = 0.1 and q will be = 1-0.1= 0.9

and n would be five or any number as a binomial experiment is repeated for a fixed number of times.

And x would take any value of n i.e.

X= 0,1,2,3,4,5

If it is 20 % . So p will be equal to = 0.2 and q will be = 1-0.2= 0.8

The probability is the number of the percent indicated. But as it is not indicated we assume it to be 10 % or 20 % .Or suppose any number for it to be a binomial experiment.

The number of trials n would be fixed .

The success remains constant for all trials.

All trials are independent.

Answer:

a

  The 95% confidence interval is  [tex]0.0503 < p < 0.1297[/tex]

b

The sample proportion is  [tex]\r p = 0.09[/tex]

c

The critical value is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

d

 The standard error is  [tex]SE =0.020[/tex]

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  200

     The number of defective is  k =  18

The null hypothesis is  [tex]H_o : p = 0.08[/tex]

The  alternative hypothesis is  [tex]H_a : p > 0.08[/tex]

Generally the sample proportion is mathematically evaluated as

            [tex]\r p = \frac{18}{200}[/tex]

            [tex]\r p = 0.09[/tex]

Given that the confidence level is  95% then the level  of significance is mathematically evaluated as

        [tex]\alpha = 100 - 95[/tex]

        [tex]\alpha = 5\%[/tex]

        [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is  

        [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the standard of error is mathematically represented as

          [tex]SE = \sqrt{\frac{\r p (1 - \r p)}{n} }[/tex]

substituting values

         [tex]SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }[/tex]

        [tex]SE =0.020[/tex]

The  margin of error is  

       [tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]

=>    [tex]E = 1.96 * 0.020[/tex]

=>   [tex]E = 0.0397[/tex]

The  95% confidence interval is mathematically represented as

     [tex]\r p - E < \mu < p < \r p + E[/tex]

=>   [tex]0.09 - 0.0397 < \mu < p < 0.09 + 0.0397[/tex]

=>  [tex]0.0503 < p < 0.1297[/tex]

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Answer:

c is the answer

Step-by-step explanation:

-3h = 31

-9h-12h = -3h

54-23= 31

Answer:

[tex]\boxed{C. -3h = 31}[/tex]

Step-by-step explanation:

Hey there!

9h - 12h = 54 - 23

Simplify

-3h = 31

C. -3h = 31

Hope this helps :)

Answer:

8 cm

Step-by-step explanation:

x:y= 2:5

x/y = 2/5

5x = 2y

y is the longer side

5x=2(20)

x=8 cm

The length of the shorter side is 8 cm.

What is rectangle?

A rectangle more generally than any quadrilateral whose axes of symmetry pass through each pair of opposite sides.This definition includes both right-angled rectangles and rectangles. Each has an axis of symmetry that is parallel and equidistant from a pair of opposite sides and a second that is a perpendicular bisector of those sides, but in the case of a crossed rectangle the first axis is not the axis of symmetry of either side. . that it divides.

Quadrilaterals that have two axes of symmetry, each passing through a pair of opposite sides, belong to the larger class of quadrilaterals that have at least one axis of symmetry through a pair of opposite sides. These quadrilaterals consist of isosceles trapezoids and crossed isosceles trapezoids (crossed quadrilaterals with the same arrangement of vertices as an isosceles trapezoid).

Given, sides of a rectangle are in ratio 2:5.

Let length of a rectangle be 5x cm and breadth of a rectangle be 2x cm.

We know length of a rectangle is longer than breadth.

So, length of the rectangle is 20 cm.

According to question,

[tex]5x = 20 \\ x = \frac{20}{5} \\ x = 4[/tex]

So, length of the rectangle (5×4) = 40 cm and breadth of the rectangle (2×4) = 8 cm.

Breath is shorter side of rectangle.

Therefore,The length of the shorter side is 8 cm.

Rectangle related one more question:

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Answer:

There has been no significant change in the number of students in each major between the last school year and this school year.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: There has been no change in the number of students.

Hₐ: There has been a significant change in the number of students.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

Here,

[tex]O_{i}[/tex] = Observed frequencies

[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.

The chi-square test statistic value is, 1.662.

The degrees of freedom is:

df = 4 - 1 = 4 - 1 = 3

Compute the p-value as follows:

[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]

*Use a Chi-square table.

The  p-value is 0.645.

The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.

Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

Answer:

Mean = 108

Median = 45

The better measure of Lauren's "typical class size" is the Mean

Step-by-step explanation:

1. Calculating mean and median.

The mean is an important measure of central tendency, and it is the average of the measurement of a given set of data. It is calculated as follows:

[tex]Mean\ (\overline {X}) &= \frac{\sum X}{N}[/tex]

where X = individual data sets

N = total number of data

[tex]Mean= \frac{375\; +\ 35\ +\ 45\ +\ 25\ +\ 60}{5} \\=\frac{540}{5} \\= 108[/tex]

The Median divides the measurements into two equal parts, and in order to calculate the median, the distribution has to first be arranged in ascending or descending order. Arranging this series in descending order:

375, 60, 45, 35, 25

The formula for calculating median is given by:

[tex]M_{d} = \frac{N\ +\ 1}{2} th\ data\\\\=\frac{5\ +\ 1}{2}th\ data\\\\=\frac{6}{2} th\ data\\= 3rd\ data\\M_{d} = 45[/tex]

from the list or arranged data in descending order (375, 60, 45, 35, 25), the third data is 45.

Therefore, Median = 45

2. The better measure of typical class size is Mean because the mean depends on all the values of the data sets, whereas the median does not. When there are extreme values (outliers) the effect on the median is very small, whereas it is effectively captured by the mean.

━━━━━━━☆☆━━━━━━━

▹ Answer

1/2k - 3/5

▹ Step-by-Step Explanation

2/5k - 3/5 + 1/10k

Collect like terms:

2/5k + 1/10k = 1/2

Final Answer:

1/2k - 3/5

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

1/2k - 3/5

Step-by-step explanation:

Hey there!

Well the only fraction needed to combine are,

2/5 and 1/10.

To add them we need to make 2/5 have a denominator of 10.

To do that we multiply 5 by 2.

5*2 = 10

What happens to the denominator happens to the denominator.

2*2 = 4

Fraction - 4/10

4/10 + 1/10 = 5/10

5/10

simplified

1/2

1/2k - 3/5

Hope this helps :)

Answer:

3x+19

Step-by-step explanation:

Let x be the unknown number

triple means 3 times

sum means add

3x+19

Answer:

17,720 ft

Step-by-step explanation:

5.4 km * (1 mile)/(1.609 km) * (5280 ft)/(1 mile) = 17,720 ft

Answer:

C.

Step-by-step explanation:

[tex]\frac{7x}{3y}+\frac{12x}{9y}[/tex]

We can reduce the second term:

[tex]\frac{7x}{3y} +\frac{4x}{3y}[/tex]

Since they now have a common denominator, we can add them:

[tex]=\frac{7x+4x}{3y}=11x/3y[/tex]

The answer is C.

So, yes, you're answer was correct!

Answer:

[tex]a = 6m/s^2[/tex]

Step-by-step explanation:

Given

When mass = 4kg; Acceleration = 15m/s²

Required

Determine the acceleration when mass = 10kg, provided force is constant;

Represent mass with m and acceleration with a

The question says there's an inverse variation between acceleration and mass; This is represented as thus;

[tex]a\ \alpha\ \frac{1}{m}[/tex]

Convert variation to equality

[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)

Make F the subject of formula;

[tex]F = ma[/tex]

When mass = 4kg; Acceleration = 15m/s²

[tex]F = 4 * 15[/tex]

[tex]F = 60N[/tex]

When mass = 10kg; Substitute 60 for Force

[tex]F = ma[/tex]

[tex]60 = 10 * a[/tex]

[tex]60 = 10a[/tex]

Divide both sides by 10

[tex]\frac{60}{10} = \frac{10a}{10}[/tex]

[tex]a = 6m/s^2[/tex]

Hence, the acceleration is [tex]a = 6m/s^2[/tex]

Answer:

(3,2)

Step-by-step explanation:

3x + 4y=17

- 4x – 3y= - 18

Multiply the first equation by 4

4(3x + 4y=17 )

12x +16y = 68

Multiply the second equation by 3

3( - 4x – 3y= - 18)

-12x -9y = -54

Add the new equations together to eliminate x

12x +16y = 68

-12x -9y = -54

-----------------------

    7y = 14

Divide by 7

7y/7 = 14/7

y=2

Now find x

3x+4(2) = 17

3x+8 = 17

Subtract 8 from each side

3x+8-8 = 17-8

3x = 9

Divide by 3

x = 3

Answer:

Step-by-step explanation:

Both functions have the same slope

The slope is m in the equation; y =mx+c which is the formula for a straight line.

m = change in Y/change in x

Using 2 points: (1,3/4) and ( 4,3) from the table;

= (3 - 3/4) / ( 4 - 1)

= 2.25/3

= 0.75 which is 3/4 which is the same as the slope of the function in the equation.

The origin is the y-intercept for the function expressed in the table.

Slope of function in table is known to be 0.75. Find c to complete equation.

3 = 0.75 ( 4) + c

3 = 3 + c

c = 0

c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.

The table and the graph express an equivalent function.

The function for the table as calculated is;

y = 0.75x + 0

y = 0.75x

This is the same as the function for the equation for the graph which is y = 3/4x.

Answer:Both functions have the same slope.

The origin is the y-intercept for the function expressed in the table.

The table and the graph express an equivalent function.

Step-by-step explanation:

Compare the linear functions expressed below by data in a table and by an equation.

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.

Which of the following statements are true?  Select all that apply.

If the equation were graphed, it would be a horizontal line.

Both functions have the same slope.

The origin is the y-intercept for the function expressed in the table.

The linear equation does not have a y-intercept.

The table and the graph express an equivalent function.

Answer:

t >± 1.895

t= 0.1705

Step-by-step explanation:

The null and alternative hypotheses are

H0: μd=0 Ha: μd>0

Significance level is set at ∝= 0.05

The critical region for  t  df=7       t >± 1.895

The test statistic under H0 is

t = d/ sd/ √n

Which has t distribution with n-1 degrees of freedom

Employee        After  Before         d = after - before        d²

1                          6         5               1                                  1

2                         6          2               4                               16

3                         7          1                6                               36

4                         7           3              4                               16

5                         4          3              1                                 1

6                         3          6              -3                               9

7                         5          3              2                               4

8                          6        7               -1                                1      

∑                                                    14                              84    

d`= ∑d/n= 14/8= 1.75

sd²= 1/8( 84- 14²/8) = 1/8 ( 84 - 24.5) = 59.5

sd= 7.7136

t= 3/ 7.7136/ √8

t= 0.1705

Since the calculated value of t= 0.1705 < ± 1.895  therefore reject the null hypothesis at 5 % significance level . On the basis of this we cannot conclude that the number of absences has declined.