5. the chi-square test for goodness of fit - no difference from a known population suppose you are reading a study conducted in the year 2000 about welfare recipients in the united states. the authors report the following frequency data on the household size of the 1,844 welfare recipients in their random sample: observed frequencies household size 5-or-more-person 4-person 3-person 2-person 1-person 203 277 301 550 513 you wonder if welfare recipients tend to live in different-sized households than the us population at large. you obtain the following data from the 2000 census: percent distribution of us households by size household size 5-or-more-person 4-person 3-person 2-person 1-person 10.83% 14.20% 16.53% 32.63% 25.81% [source: hobbs f., & Stoops, N. (2002). Census 2000 special reports: Demographic trends in [Source: the 20th century. U.S. Census Bureau.] You use a chi-square test for goodness of fit to see how well the sample of welfare recipients fits the census data. What is the most appropriate null hypothesis? O The distribution of household sizes among welfare recipients is the same as that provided by the census data. The distribution of household sizes among welfare recipients is equal across the five household-size categories. O The distribution of household sizes among welfare recipients is different from that provided by the census data. O The distribution of household sizes among welfare recipients is not equal across the five household-size categories. Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 1,844, if the null hypothesis is true: Expected Frequencies Household Size 5-or-more-person 4-person 3-person 2-person 1-person 475.94 304.81 601.70 The chi-square statistic has been calculated for you: x2 = 8.31. The distribution of the chi-square statistic has degrees of freedom. Use the following Distributions tool to find the critical value. Chi-Square Distribution Degrees of Freedom = 4 4 10 11 12 13 14 With the level of significance a = .01, the critical value is Because the chi-square statistic x2 is the critical value, you the null hypothesis. Therefore, you conclude that the proportions of welfare recipients in the five household-size categories differ from the corresponding proportions for all U.S. households.

Applying the distance formula, the distance between the two points (7, 4) and (3, 3) is: 4 units.

If we have two given points with their coordinates, to find the distance between these two points, apply the distance formula that is expressed as:

d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

Given the two points:

(7, 3) = [tex](x_1, y_1)[/tex]

(3, 3) = [tex](x_2, y_2)[/tex]

Substitute the values into the distance formula:

d = √[(3−7)² + (3−3)²]

d = √[(−4)² + (0)²]

d = √16

d = 4 units.

The distance is: 4 units.

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Answer: 480 are teenagers

Step-by-step explanation:

To find a percentage of a number, I like to convert the percentage into its decimal form, so I do...

10% = .1 because a percentage is out of a whole number. 100% = 1.

Next, multiply your sum by the percentage you are looking for, so...

[tex]4800*.1=480[/tex]

The null hypothesis is that the mean is equal to 7.6 lbs while the alternate hypothesis of the valve is that it is not equal to 7.6lbs.

What is a Hypothesis in statistics?

This term is used to refer to a statement which is made that is tested to be true or untrue during the study.

The Null hypothesis

H0: μ = 7.6

The alternate hypothesis:

H1: μ ≠ 7.6

The null hypothesis says the valve produces a mean pressure of 7.6 lbs. The alternate hypothesis on the other hand says that it does not equal to 7.6lbs.

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Answer:

H0: μ=7.6

Ha: μ>7.6

Answer: 8

Step-by-step explanation:

We only need to take  672/84 = 8

So there are 8

If you can please give me a Brainliest, I only need 1 more to become an Ace, thank you!

Answer:

x=8

Step-by-step explanation:

Lets assume that the number of 84 is x

as given in this equation

total values given in the question be 672

then the equatiuon becomes

84 multiplied by x is 672

simplify above the equation

84x=672

[tex]x=\frac{62}{84}[/tex]

x=8

Therefore, the number of 84 is 672 is 8.

(Hope this helped! :D)

Making predictions about your data requires the usage of a hypothesis. They aid data analysts in determining what they want to verify or dispute.

Given,

A senior data analyst requests that a junior data analyst offer two hypotheses for a project involving data analytics.

The rationale for a hypothesis must be explained;

This is,

Hypothesis testing is a sort of statistical reasoning that uses information from a sample to draw conclusions about a population parameter or population probability distribution. The parameter or distribution is initially best guessed.

Here,

A hypothesis seeks to infer something from your data. Data analysts use them to show or refute what they want to prove.

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Answer:39cm

Step-by-step explanation:

Answer:

(6,-2)

Step-by-step explanation:

The point is now 6 units to the right of the y axis.  That would be 6, but the y value would be the same 2 units below the x axis.

The maximum error in the area is 33.933 sq cm. The relative error is 0.0148. The percent error will be 1.48%.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

1)  A = pi(r²)

dA = 2(pi)r(dr)

= 2(3.14)(27)(0.2) sq cm

= 33.93 sq. cm

2)  Relative error is the above divided by actual area

actual area=3.14*27*27

=2289.06 sq cm

Relative error=0.0148

3) % error -- convert the above to a % by appropriate shifting of decimal point

% error=0.0148*100

=1.48%

The area's largest inaccuracy is 33.933 sq cm. 0.0148 is the relative inaccuracy. There will be a 1.48% error percentage.

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Answer: 21.78

Step-by-step explanation:

25.65 - 3.87 = 21.78

A sample of 68  is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean for the standard deviation of 40 hours

Since a level =1-0.96/2 =0.02, here the  Z value of 1-a = 1-0.02= 0.98 , for which z=2.055 .Now we know that the formula for margin is:

M = z*σ/√n, where σ is the standard deviation and n is the sample size since we are provided with the standard deviation of  40  and M=10. so,

=> 10= 2.055*40/√n

=>10√n= 2.055*40

=>√n =  82.2/10

=>n=67.6 ,which is almost  68

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Answer:

1/2x+3/4y=10

ANS:

x=

−3

2

y+20

Let's solve for x.

1

12

12x+

12x+3

12x+34

12x+34y=10

Step 1: Add (-3)/4y to both sides.

1

12

12x+

12x+3

12x+34

12x+34y+

12x+34y+−3

12x+34y+−34

12x+34y+−34y=10+

12x+34y+−34y=10+−3

12x+34y+−34y=10+−34

12x+34y+−34y=10+−34y

12x+34y+−34y=10+−34y1

12x+34y+−34y=10+−34y12

12x+34y+−34y=10+−34y12x=

12x+34y+−34y=10+−34y12x=−3

12x+34y+−34y=10+−34y12x=−34

12x+34y+−34y=10+−34y12x=−34y+10

Step 2: Divide both sides by 1/2.

1

2

x

x1

x12

x12=

x12=−3

x12=−34

x12=−34y+10

x12=−34y+101

x12=−34y+1012

x12=−34y+1012x=

x12=−34y+1012x=−3

x12=−34y+1012x=−32

x12=−34y+1012x=−32y+20

Answer:

Answer:x=

Answer:x=−3

Answer:x=−32

Answer:x=−32y+20

question

Answer:

Usually we write the final answer with positive exponents.

[tex]\frac{1}{x^{2} }[/tex]

Step-by-step explanation:

[tex]\frac{x^{5} }{x^{7} }[/tex]

When we are dividing powers with the same bases, we subtract the exponents.

[tex]x^{5-7}[/tex] = [tex]x^{-2}[/tex] or [tex]\frac{1}{x^{2} }[/tex]

Answer:

11.3

Step-by-step explanation:

Angles A & B are each 45 degrees because if you subtract 90 from 180 and divide that by 2 you get 45 then you do:

sin(45) times 16 which is 11.3

SIN = opposite over hypotenuse.

Answer:

what is the question??????

A system of linear inequalities for the number of packages of both hot dogs and hamburgers that can be bought is as follows:

x + y ≥ 3.

4x + 5y ≤ 20.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of hamburgers respectively, and then translate the word problem into algebraic equation as follows:

Since you will need at least 3 packages of both hot dogs and hamburgers, the linear inequality to represent this is as follows:

x + y ≥ 3.

For the cost of both hot dogs and hamburgers, and the maximum amount you can spend;

4x + 5y ≤ 20.

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Answer:

y=35

Step-by-step explanation:

3y+25+2y+30+2y-5+y+30=360

Combine like terms then you will get
8y+80=360
8y=280

y=35

Answer:

35°

Step-by-step explanation:

the sum of the angles in a quadrilateral is 360 degrees

let 's make and solve the equation

3y + 25 + 2y + 30 + 2y - 5 + y +30 = 360

Combine like terms then you will get

(3y + 2y + 2y + y) + (25 + 30 - 5 + 30) = 360

8y + 80 = 360

8y + 80 - 80 = 360 - 80

8y = 280

y = 280:8

y= 35

Answer:

x = -2, y = -3

Step-by-step explanation:

Solve for y:

If -3x + 9y = -21, and -3x +8y = -18, then -21 - y = -18

Add 18 to both sides:

-3 - y = 0, so y = -3

reconstruct new equation:

-3x + 9(-3) = -21, -3x + 8(-3) = -18

-3x + -27 = -21, -3x + -24 = -18

Using the new equation, solve for x:

add 24 to both sides of each equation :

-3x + -3 = 3, -3x = 6

x=-2

The one - year standard deviation is, 10.45%.

what is standard deviation?

The standard deviation in statistics is a measurement of how much a set of values can vary or be dispersed. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.

Given:

A portfolio has a 3-year standard deviation of 18.1%.

We have to find the one - year standard deviation.

One - year SD = Variance / number of years.

Here,

Variance = square of standard deviation = (18.1)^2 = 327.61

So,

One - year SD = 327.61 / (3/1)

One - year SD = 109.20

Now,

(109.2)^(1/2) = 10.45%

Hence, the one - year standard deviation is, 10.45%.

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Answer:

b)-8

Step-by-step explanation:

Because the absolute value of -8 is 8 and it will have an greater number then all of them

5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).

When we use the formula A = A0(1 - r)t,

(1/2)A₀ = A₀(1 - 0.11)t

[Divide both sides by A₀ results in:

1/2 = (0.87)t

Using the log of both sides;:

log(1/2) = log(0.87)t

Using a logarithm property, we can bring the "t" to the front, giving us:

log(1/2) = t.log(0.89)

[Dividing both sides with log(0.89) gets us:

t =  log(1/2)/log(0.89)

Using calculator for soling the values.

t = 5.94 seconds

Thus, 5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).

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The basketball player made 15 errors in  100 games as of the given condition.

Given that,
A baseball player made 9 errors in 60 games, how many errors would we expect the player to make in 100 games is to be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Let the error be x, for 100 games,
Now, according to ot the question,
9/60= x / 100
x = 15

Thus, the basketball player made 15 errors in  100 games.

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Using the binomial distribution, it is found that there is a 0.5954 = 59.54% probability that at least 1 is defective.

What is the binomial distribution?

A collection of numerous independently distributed Bernoulli trials with equal distributions results in the binomial distribution. The experiment in a Bernoulli trial is said to be random and can only result in one of two outcomes: success or failure.

For each phone, there are only two possible outcomes, either it is defective, or it is not. The probability of a phone being defective is independent of any other phone, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_n, x. p^{x.(1-p)^n-x}[/tex]

[tex]C_n, x = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of success on a single trial.

In this problem:

0.11 probability of a single phone is defective, hence

6 phones are selected at random, hence

The probability that at least 1 is defective is:

P(X >= 1) = 1 - P(X = 0)

In which

[tex]P(X = x) = C_n, x. p^{x.(1-p)^n-x}[/tex].

P(x = 0) = C₆,₀.(0.11)⁰ (0.86)⁶ = 0.4046

Then:

P(X >= 1) = 1 - P(X = 0) = 1 - 0.4046 = 0.5954

Hence, the 0.5954 = 59.54% probability that at least 1 is defective.

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Answer:

30

Step-by-step explanation:

9-(-21) = 9+21 = 30

When a pair of dice is rolled, there is a 1/6 chance that the result will be less than 5.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Here,

Total possibility=36

To calculate the probability correctly, the list should be,

(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)

Total cases=6

probability of getting a sum less than 5,

=6/36

=1/6

The probability of getting a sum less than 5 when a pair of dice is rolled will be 1/6.

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The population size after four days is 121.

Given that,

a population of protozoa with a constant relative growth rate of 0.8603 per member per day

let P be the population size and let t be the time interval then the given system modeled by the differential equation

[tex]\frac{dP}{dt}[/tex] = 0.8603

by solving the separable equation and expifying both sides we get,

P = A [tex]e^{0.8603t}[/tex]

From the condition that on day zero the population consist of four members,

i.e. P(0) = 4, A = 4

Therefore population size after four days is

P(4) = 4[tex]e^{4(0.8603)}[/tex]

      = 4 [tex]e^{3.441}[/tex]  

      = 4 × 30.295

P(4) =  121.2

nearest whole number is 121

i.e P(4) = 121

Hence the population size after four days is 121.

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The odds in favor of her selecting a red marble = 6/7

Here, Madison has a bag with 30 red marbles and 5 green marbles. she chooses one at random.

We need to decide the odds in favor of her selecting a red marble.

Total number of marbles = 30 + 5

Total number of marbles = 35

So, the odds in favor of her selecting a red marble would be,

p = number of favourable outcomes / total number of outcomes

p = 30/35

p = 6/7

Therefore, the probability that she select a red marble is 6/7

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Answer: 67 87 34

Step-by-step explanation:

Each candy costs $3 and each pretzel costs $4.25

From the question, we are to determine the price of each candy and the price of each pretzel

Let the price of each candy be x and the price of each pretzel be y

From the given information,

3 candies and 2 pretzels cost $17.50

Then, we can write that

3x + 2y = 17.50          ----------- (1)

Also,

9 candies and 4 pretzels cost $44

Then,

9x + 4y = 44              ------------ (2)

Solve the equations simultaneously

Multiply equation (1) by 2 and subtract it from equation (2)

2 × [3x + 2y = 17.50

6x + 4y = 35

Subtract from equation (2)

9x + 4y = 44

- [6x + 4y = 35

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

3x + 0 = 9

3x = 9

Divide both sides by 3

3x/3 = 9/3

x = 3

substitute the value of x into equation (2)

9x + 4y = 44  

9(3) + 4y = 44  

27 + 4y = 44

4y = 44 - 27

4y = 17

y = 17/4

y = 4.25

Hence, the cost of the candy is $3 and the cost of the pretzel is $4.25

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a)The two way table is shown in figure,

b)The success rate of the three treatments in preventing cardiac arrests are 90.91% , 79.41% and 70%.

c)The expected cell count are as shown in the figure,

d)No. There is no difference among the treatments.

e) The brief summary is mentioned below.

Given,

The total number of people is 107.

33 people are enrolled in a stress management programme.

3 people had cardiac events as a result of the stress management programme.

34 people are in the exercise group.

The number of cardiac events in the exercise group was 7 people.

40 people receive routine care.

12 people had cardiac events while receiving standard care.  

a)

The two-way table for the given information is shown in the figure

b)

During the same time period, 7 of the 34 people in the exercise group and 12 of the 40 patients in usual care experienced such events.Success rate can be determined by,

[tex]Success=\frac{no.\ of\ people\ who\ did not\ suffered\ in\ group}{Total\ number\ of people\ in\ group}[/tex]

For stress management:-

[tex]Success\ rate = \frac{30}{33}=0.9091=90.90\%[/tex]

For exercise program:-

[tex]Success\ rate = \frac{27}{34}=0.7941=79.41\%[/tex]

For usual care:-

[tex]Success\ rate = \frac{28}{40}=0.7=70\%[/tex]

c)

Expected cell count can be calculated by formula,

[tex]Expected\ value=\frac{row\ total*column\ total}{table\ total}[/tex]

then,

Expected value for the people who suffered cardiac arrest,

Under stress management:-

[tex]E= \frac{22*23}{107}=6.79[/tex]

Under exercise group:-

[tex]E=\frac{22*34}{107}=6.99[/tex]

Under usual care:-

[tex]E=\frac{22*40}{107}=8.22[/tex]

Expected value for the people who did not suffered cardiac arrest :-

Under stress management:-

[tex]E=\frac{85*33}{107}=26.21[/tex]

Under exercise group:-

[tex]E=\frac{85*34}{107}=27.01[/tex]

Under usual care:-

[tex]E=\frac{85*40}{107}=31.78[/tex]

The expected cell count is mentioned in the table

d)

The null and alternate hypothesis are

[tex]H_0[/tex] :There is no difference in the actual success rates of the three treatments.

[tex]H_1[/tex] :The three treatments differ in terms of actual success rates.

The test statistic can be calculated by

[tex]x^2=\sum \frac{(O-E)^2}{E}[/tex]

Where,

O=observed value

E=Expected value

Under null hypothesis,

[tex]x^2=\frac{(3-.679)^2}{6.79}+\frac{(7-6.99)^2}{6.99}+\frac{(12-8.22)^2}{8.22}+\frac{(30-26.21)^2}{26.21}+\frac{(27-27.01)^2}{27.01}+\frac{(28-31.78)^2}{31.78}\\\\=4.8514[/tex]

The p-value for the test is [tex]P(x_2 > 4.8514)=0.0884[/tex]

There is no statistically significant difference in the success rates of the three treatments.

e)

Because the p-value is greater than 0.05 (at the 5% level of significance), there is insufficient evidence to reject the null hypothesis and conclude that there is no difference in the actual success rates for the treatments.

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