Method 1: Long Division (x^2+3x-43) / (x+8
Answers
Answer:
x - 5 - (3/x+8)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Related Questions
Marta recorded the temperature at 8 p.m. as 56°F and the temperature at 8 a.m. the next morning as 36°F. Marta assumed the temperature changed at a constant rate. She wrote an equation to find the number of degrees the temperature dropped each hour, h, of the night. Which equation did Marta write?
Answers
Answer: 5h/3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Answer:
5h 3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
The author purchased a slot machine (Bally Model 809) and tested it by playing it 1197 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of x^2 = 8.185 . Use α= 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as expected?
Answers
Answer:
No the slot machine doesn't appear to function as expected.
Step-by-step explanation:
From chi-squared table , for 9 degrees of freedom and alpha 0.05,
critical value is, 3.325.
Since observed value is greater than critical value we can say that actual outcomes do not agree with the expected frequencies. The slot machine doesn't appear to function as expected.
4 lines are shown. A line with points A, F, D intersects with a line with points B, F, E at point F. A line extends from point F to point G between angle E F D. Another line extends from point F to point D in between angle B F D. In the diagram, which angle is part of a linear pair and part of a vertical pair? AngleBFC AngleCFG AngleGFD AngleEFA
Answers
Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.
What are linear pair and part of a vertical pair?If two angles is said to create a linear pair, the angles are then regarded as supplementary and it is said that their measures often add up to 180°.
Note that Vertical angles are said to be pair of nonadjacent angles created by the crossing or the intersection of any two straight lines.
Since vertical angles are seen if "X" created by two straight lines then when you look at the image attached, you can see that the angle that can from this is Angle EFA.
Therefore, Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.
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From an urn containing 3 white and 2 black balls, two balls are drawn one after the other without replacement. What is the probability that the first ball drawn is white and the second black?
Answers
Answer:
There is a 3/5 chance of the first ball being white, and a 3/10 chance the second one is black.
Step-by-step explanation:
There are 5 balls, of which 3 are white, so you have a 3/5 chance of the first one being white. Then you have 2 white and 2 black balls. There is a 2/4 chance of picking a black ball. Multiply 3/5 and 2/4 to get 6/20, or 3/10 for choosing a white ball then a black ball.
A random sample of 150 mortgages in the state of Florida was randomly selected. From this sample, 17 were found to be delinquent on their current payment. The 98% confidence interval for the proportion based on this sample is ________.
Answers
Answer:
The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 150, \pi = \frac{17}{150} = 0.1133[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 - 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.0531[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 + 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.1735[/tex]
The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).
Solve seven square root three plus two square root nine and explain whether the answer is rational or irrational
Answers
Answer:
Step-by-step explanation:
5
What is equal to 5x when x is equal 50
Answers
If X=50 then you would do 5x50=250
Answer:
250
Step-by-step explanation:
if x=50
5(x)=5*50=250
Hope it helps..Pls mark as Brainliest!!
Do all perpendicular lines have negative reciprocal slopes?
Answers
Not necessarily, the more correct definition is opposite reciprocal slopes.
The example used is how horizontal and vertical lines are parallel. Horizontal lines have a slope of 0, also written as 0/1. However, vertical lines have an undefined slope, which isn't necessarily negative. It has a slope of 1/0, which is undefined. In this case, the reciprocal isn't negative.
In all other cases (1 and -1, 2 and -1/2, etc.) yes, the perpendicular pairs are negative and reciprocal.
Which table represents a linear function?
Answers
Answer:
Top right option
Step-by-step explanation:
The total claim amount for a health insurance policy follows a distribution with density function 1 ( /1000) ( ) 1000 x fx e− = , x > 0. The premium for the policy is set at the expected total claim amount plus 100. If 100 policies are sold, calculate the approximate probability that the insurance company will have claims exceeding the premiums collected.
Answers
Answer:
the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Step-by-step explanation:
The probability of the density function of the total claim amount for the health insurance policy is given as :
[tex]f_x(x) = \dfrac{1}{1000}e^{\frac{-x}{1000}}, \ x> 0[/tex]
Thus, the expected total claim amount [tex]\mu[/tex] = 1000
The variance of the total claim amount [tex]\sigma ^2 = 1000^2[/tex]
However; the premium for the policy is set at the expected total claim amount plus 100. i.e (1000+100) = 1100
To determine the approximate probability that the insurance company will have claims exceeding the premiums collected if 100 policies are sold; we have :
P(X > 1100 n )
where n = numbers of premium sold
[tex]P (X> 1100n) = P (\dfrac{X - n \mu}{\sqrt{n \sigma ^2 }}> \dfrac{1100n - n \mu }{\sqrt{n \sigma^2}})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{\sqrt{n}(1100-1000}{1000})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{10*100}{1000})[/tex]
[tex]P(X>1100n) = P(Z> 1) \\ \\ P(X>1100n) = 1-P ( Z \leq 1) \\ \\ P(X>1100n) =1- 0.841345[/tex]
[tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Therefore: the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Which of the lists of letters all have rotational symmetry?
a. C, H, N, X
b. N, O, S, Z
c. H, J, N, S
d. F, H, X, Z
Answers
Answer:
So C doesn't have symmetry so that rules out a
b does though
J doesn't work so that rules out c
F doesn't work so that rules out d
B is answer
Answer:
B. is the rotational symmetry
Step-by-step explanation:
Explain how to find the range of a data set. Choose the correct answer below. A. The range is found by subtracting the first data entry from the last data entry. B. The range is found by adding the first and last data entries. C. The range is found by subtracting the minimum data entry from the maximum data entry. D. The range is found by adding the minimum and maximum data entries.
Answers
Answer:
C
Step-by-step explanation:
The range of a data set is the difference between the biggest and smallest values, so to find it, you just subtract the minimum from the maximum.
What’s the correct answer for this question?
Answers
Answer:
C.
Step-by-step explanation:
Diameter = 11 inches.
Radius = D/2 = 5.5 inches
Volume = 4/3πr³
= 4/3(3.14)(5.5)³
= 696.6 in.³
List the important features for the graph of a quadratic function.
Answers
Answer:
VertexMinimum PointMaximum PointRootsAxis of SymmetryStep-by-step explanation:
The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.
The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.
The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.
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The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The important features for the graph of a quadratic function will be
The parabola is symmetric about the line which is passing through focus.
The quadratic function can be expressed in the form of vertex form.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
More about the quadratic equation link is given below.
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Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 25 years?
Answers
Answer:
Step-by-step explanation:
[tex]100 (0.96)^{25} =[/tex] around 36.04
If you vertically stretch the exponential function f(x)=2x by a factor of 3, what is the equation of the new function
Answers
Answer:
g(X)=3(2^x)
Step-by-step explanation:
The article "A Shovel with a perforated blade reduces energy expenditure required for digging wet clay" (Human Factors, 2010:492-502) reported on an experiment in which each of 13 workers was provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on stable energy expenditure (measured in kilocalories per kg of subject per pounds of clay):
1 2 3 4 5 6 7 8 9 10 11 12 13 Worker Conventional 0.0011 0.0014 0.0018 0.0022 0.001 0.0016 0.0028 0.002 0.0015 0.0023 0.0017 0.002 0.0014 Perforated 0.0011 0.001 0.0019 0.0013 0.0011 0.0017 0.0024 0.002 0.0013 0.0017 0.002 0.0013 0.0013 Carry out a test of hypotheses at significance level 0.05 to see whether the true average energy expenditure using the conventional shovel exceeds that using the perforated shovel. (hint: this is a paired-design!). Make sure to calculate a p-value!
Answers
Answer:
Step-by-step explanation:
Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.
The data for the test are the differences between the true average energy expenditures of the shovels.
μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.
Conventional perforated diff
0.0011 0.0011 0
0.0014 0.0010 0.0004
0.0018 0.0019 -0.0001
0.0022 0.0013 0.0009
0.0010 0.0011 -0.0001
0.0016 0.0017 -0.0001
0.0028 0.0024 0.0004
0.0020 0.002 0
0.0015 0.0013 0.0002
0.0023 0.0017 0.0006
0.0017 0.002 -0.0003
0.0020 0.0013 0.0007
0.0014 0.0013 0.0001
Sample mean, xd
= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077
xd = 0.0002077
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923
Standard deviation = √(0.00000158923/13
sd = 0.00035
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (0.0002077 - 0)/(0.00035/√13)
t = 2.14
We would determine the probability value by using the t test calculator.
p = 0.027
Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.
A jury pool has 15 men and 21 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of:_____
(a) all men
(b) all women
(c) 8 men and 4 women
(d) 6 men and 6 women
Give all answers accurate to four decimal places.
Answers
Answer:
(a) all men = 3.6351 * 10^ -7
(b) all women = 2.3483* 10^ -4
(c) 8 men and 4 women = 0.0308
(d) 6 men and 6 women= 0.2170
Step-by-step explanation:
A jury pool has 15 men and 21 women, from which 12 jurors will be selected.
Total = 36 people
Probability of
(a) all men
= 15C12/36C12
= 455/1251677700
= 3.6351 * 10^ -7
(b) all women
= 21C12/36C12
= 293930/1251677700
= 2.3483* 10^ -4
(c) 8 men and 4 women
=( 15C8 * 21C4)/36C12
= (6435*5985)/1251677700
= 38513475/1251677700
= 0.0308
(d) 6 men and 6 women
= (15C6 * 21C6)/(36C12)
= (5005*54264)/1251677700
= 271591320/1251677700
= 0.2170
Explain what the number 0 on the gauge represents and explain what the numbers above 0 represent
Answers
help as quick as possible 18 points :)
Answers
Answer:
Step-by-step explanation:
1/10*5 is the answer i think...
What is the sum of 1/6 and 1/7
Answers
1/6 + 1/7 = 13/42
aka: 7/42 + 6/42
Answer:
13/42
Step-by-step explanation:
1/6 + 1/7
We need a common denominator of 42
1/6 *7/7 + 1/7 *6/6
7/42 + 6/42
13/42
help asap giving branlist!!!
Answers
Answer:
option 2
Step-by-step explanation:
Because (0, 900) is a point on the line it means that it costs $900 to make the commercial. A slope of 110 means that they pay $110 every time it's aired so the answer is Option 2.
Use z scores to compare the given values. The tallest living man at one time had a height of 252 cm. The shortest living man at that time had a height of 79.2 cm. Heights of men at that time had a mean of 176.74 cm and a standard deviation of 8.06 cm. Which of these two men had the height that was moreâ extreme?
Answers
Answer:
The more extreme height was the case for the shortest living man at that time (12.1017 standard deviation units below the population's mean) compare with the tallest living man (at that time) that was 9.3374 standard deviation units above the population's mean.
Step-by-step explanation:
To answer this question, we need to use standardized values, and we can obtain them using the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
x is the raw score we want to standardize.[tex] \\ \mu[/tex] is the population's mean.[tex] \\ \sigma[/tex] is the population standard deviation.A z-score "tells us" the distance from [tex] \\ \mu[/tex] in standard deviation units, and a positive value indicates that the raw score is above the mean and a negative that the raw score is below the mean.
In a normal distribution, the more extreme values are those with bigger z-scores, above and below the mean. We also need to remember that the normal distribution is symmetrical.
Heights of men at that time had:
[tex] \\ \mu = 176.74[/tex] cm.[tex] \\ \sigma = 8.06[/tex] cmLet us see the z-score for each case:
Case 1: The tallest living man at that time
The tallest man had a height of 252 cm.
Using [1], we have (without using units):
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{252 - 176.74}{8.06}[/tex]
[tex] \\ z = \frac{75.26}{8.06}[/tex]
[tex] \\ z = 9.3374[/tex]
That is, the tallest living man was 9.3374 standard deviation units above the population's mean.
Case 2: The shortest living man at that time
The shortest man had a height of 79.2 cm.
Following the same procedure as before, we have:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{79.2 - 176.74}{8.06}[/tex]
[tex] \\ z = \frac{-97.54}{8.06}[/tex]
[tex] \\ z = -12.1017[/tex]
That is, the shortest living man was 12.1017 standard deviation units below the population's mean (because of the negative value for the standardized value.)
The normal distribution is symmetrical (as we previously told). The height for the shortest man was at the other extreme of the normal distribution in [tex] \\ 12.1017 - 9.3374 = 2.7643[/tex] standard deviation units more than the tallest man.
Then, the more extreme height was the case for the shortest living man (12.1017 standard deviation units below the population's mean) compare with the tallest man that was 9.3374 standard deviation units above the population's mean.
Account A and Account B both have a principal of $2,000 and an annual interest rate of 5%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?
Answers
Answer:
Which earns more interest = Account B
How much more = $1,306.60
Step-by-step explanation:
Given;
Principal P = $2,000
Interest rate r = 5% = 0.05
Time t = 20 years
For account A;
Simple interest = P×r×t
Substituting the values;
Simple interest = 2,000 × 0.05 × 20 = $2000
Interest on account A = $2,000
For account B;
Compound interest
Final amount = P(1 + r)^t
Since it's compounded annually
Substituting the values;
Final amount = 2000(1+0.05)^20
Final amount = $5306.60
Interest = final amount - principal = $5306.60 -$2000
Interest = $3,306.60
Therefore, account B earns more interest.
Difference = account B interest - account A interest
Difference = $3,306.60 - $2,000
Difference = $1,306.60
8. Nate bought two large pizzas and one small pizza and paid $36. If the difference in cost between a large and small pizza is $5.25, how much does a small pizza cost?
Answers
Answer:
$8.5
Step-by-step explanation:
We need to propose a system of equations with the information provided to us.
two large pizzas and one small pizza cost $36:
[tex]2L+S=36[/tex]
where
[tex]L[/tex]: Large pizza
[tex]S:[/tex] Small pizza
and the difference in cost between a large and small pizza is $5.25:
[tex]L-S=5.25[/tex]
our system of equations is:
[tex]2L+S=36[/tex]
[tex]L-S=5.25[/tex]
We are asked for the price of small pizza, so we must manipulate the equations in such a way that adding or subtracting them removes the variable L and we are left with an equation for S.
Multiply the second equation of the system by -2
[tex](-2)(L-S=5.25)\\\\-2L+2S=-10.5[/tex]
and now we sum this with the first equation of the system:
[tex]-2L+2S=-10.5\\+(2L+S=36)\\-------------\\-2L+2L+2S+S=-10.5+36[/tex]
simplifying the result:
[tex]3S=25.5[/tex]
and solving for S (the price of a small pizza)
[tex]S=25.5/3\\S=8.5[/tex]
An AP news service story, printed in the Gainesville Sun on May 20, 1979, states the following with regard to debris from Skylab striking someone on the ground: "The odds are 1 in 150 that a piece of Skylab will hit someone. But 4 billion people ... live in the zone in which pieces could fall. So any one person’s chances of being struck are one in 150 times 4 billion—or one in 600 billion." Do you see any inaccuracies in this reasoning?
Answers
Answer:
The odds are one in approximately 27 million.Not one in 600 billionStep-by-step explanation:
From the news story, we are told that:
The odds are 1 in 150 that a piece of Skylab will hit someone.
However, 4 billion people live in the zone in which pieces could fall.
Therefore, any one person’s chances of being struck are:
[tex]=\dfrac{1}{150} \times 4$ billion\\=\dfrac{1}{37.5}$ billion\\\\=26,666,667 million[/tex]
Therefore, the odds are one in approximately 27 million.
The inaccuracy presented in this reasoning was that the odds are one in 600 billion.
Round the following number to the nearest thousand 2385
Answers
By rounding of the following number to the nearest thousand is 2000.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
'
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
Round the following number to the nearest thousand
2385
= 2000
Thus, by rounding of the following number to the nearest thousand is 2000.
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I need help pleaseeee help meee
Answers
Answer:
x>-1
Step-by-step explanation:
Answer:
x > -1
Step-by-step explanation:
First we need to determine what sign this inequality uses:
A closed circle represents greater than or equal to (≥) or less than or equal to (≤)An open circle represent greater than (>) or less than (<)Here we have an open circle so we know our sign will either be > or <
Our point is on the -1, and the arrow points in the direction of the sign as long as the variable x is on the left side of the answer
So the arrow is point to the right, indicating our sign will also be "pointing" to the right (>)
The inequality of this graph reads: x > -1
Jan's All You Can Eat Restaurant charges $9.10 per customer to eat at the restaurant. Restaurant management finds that its expense per customer, based on how much the customer eats and the expense of labor, has a distribution that is skewed to the right with a mean of $8.10 and a standard deviation of $4.
A. If the 100 customers on a day have the characteristics of the random sample from their customer base, find the mean and standard error of the sampling distribution of the restaurant's sample mean expense per customer.
B. Find the probability that the restaurant makes a profit that day, with the sample mean expense being
less than $8.95.
Answers
Answer:
Step-by-step explanation:
From the given question;
Given that:
Jan's All You Can Eat Restaurant charges $9.10 per customer to eat at the restaurant.
Distribution is skewed and and has a mean of $8.10 and a standard deviation of $4.
A. If the 100 customers on a day have the characteristics of the random sample from their customer base, find the mean and standard error of the sampling distribution of the restaurant's sample mean expense per customer.
the mean by using the central limit theorem is 8.10
the standard error of the sampling distribution = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
the standard error of the sampling distribution = [tex]\dfrac{4}{\sqrt{100}}[/tex]
= 4/10
= 0.4
B.
P(X > $8.95) = P (Z > 8.95 - 8.10/0.4)
P(X > $8.95) = P (Z > 2.1)
P(X > $8.95) = 1 - P (Z < 2.1)
P(X > $8.95) = 1 - 0.9821
P(X > $8.95) = 0.0179
It has been suggested that night shift-workers show more variability in their output levels than day workers. Below, you are given the results of two independent random samples.
Night Shift (N) Day Shift (D)
Sample Size 9 8
Sample Mean 520 540
Sample Variance 38 20
Required:
a. At 95% confident level, what is the critical value?
b. State the null and alternative hypotheses to be tested.
c. Compute the test statistic.
d. Determine the p-value.
Answers
Answer:
Null hypotheses = H₀ = σ₁² ≤ σ₂²
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic = 1.9
p-value = 0.206
Since the p-value is greater than α therefore, we cannot reject the null hypothesis.
So we can conclude that the night shift workers don't show more variability in their output levels than day workers.
Step-by-step explanation:
Let σ₁² denotes the variance of night shift-workers
Let σ₂² denotes the variance of day shift-workers
State the null and alternative hypotheses:
The null hypothesis assumes that the variance of night shift-workers is equal to or less than day-shift workers.
Null hypotheses = H₀ = σ₁² ≤ σ₂²
The alternate hypothesis assumes that the variance of night shift-workers is more than day-shift workers.
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic:
The test statistic or also called F-value is calculated using
Test statistic = Larger sample variance/Smaller sample variance
The larger sample variance is σ₁² = 38
The smaller sample variance is σ₂² = 20
Test statistic = σ₁²/σ₂²
Test statistic = 38/20
Test statistic = 1.9
p-value:
The degree of freedom corresponding to night shift workers is given by
df₁ = n - 1
df₁ = 9 - 1
df₁ = 8
The degree of freedom corresponding to day shift workers is given by
df₂ = n - 1
df₂ = 8 - 1
df₂ = 7
We can find out the p-value using F-table or by using Excel.
Using Excel to find out the p-value,
p-value = FDIST(F-value, df₁, df₂)
p-value = FDIST(1.9, 8, 7)
p-value = 0.206
Conclusion:
p-value > α
0.206 > 0.05 ( α = 1 - 0.95 = 0.05)
Since the p-value is greater than α therefore, we cannot reject the null hypothesis corresponding to a confidence level of 95%
So we can conclude that the night shift workers don't show more variability in their output levels than day workers.