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Peter rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 11.

Answer:

[tex] p_v= 0.01[/tex]

Since the significance level is 0.05 we see that [tex]pv<\alpha[/tex] so we have enough evidence to reject the null hypothesis. And the best conclusion for this case would be:

b. at least some, but not all, of the gestation periods across all four species are the same

Because is only to identify if AT LEAST one mean is different, NOT to conclude that the all the means are different.

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

Solution to the problem

The hypothesis for this case are:

Null hypothesis: [tex]\mu_{A}=\mu_{B}=\mu_{C}= \mu_D[/tex]

Alternative hypothesis: Not all the means are equal [tex]\mu_{i}\neq \mu_{j}, i,j=A,B,C,D[/tex]

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have [tex]p=4[/tex] groups and on each group from [tex]j=1,\dots,p[/tex] we have [tex]n_j[/tex] individuals on each group we can define the following formulas of variation:  

[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]  

[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]  

[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]  

And we have this property  

[tex]SST=SS_{between}+SS_{within}[/tex]  

And in order to test this hypothesis we need to ue an F statistic and for this case the p value calculated is

[tex] p_v= 0.01[/tex]

Since the significance level is 0.05 we see that [tex]pv<\alpha[/tex] so we have enough evidence to reject the null hypothesis. And the best conclusion for this case would be:

b. at least some, but not all, of the gestation periods across all four species are the same

Because is only to identify if AT LEAST one mean is different NOT to conclude that the all the means are different.

The correct option is (d)not all of the average gestation periods are the same across all four species.

In a test of hypothesis, the test statistic is a function of the sample data used to decide whether or not to reject the null hypothesis.

Given that,

[tex]\alpha=0.05\\p-value=0.009[/tex]

[tex]H_0:[/tex]The average gestation period is the same for each of the four spices.

Since the p-value is less than the value of the [tex]\alpha[/tex].

So, we reject the [tex]H_0[/tex]

Not all of the average gestation periods are the same across all four species.

Learn more about the topic Test Statistic:

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Answer:

5 inches.

Step-by-step explanation:

We know that the circumference of a circle is equivalent to πr² or πd.

We need to know the radius given the circumference.

C = πr²

75 = 3.14(r^2)    (Divide both sides by 3.14)

23.88535031847134 = r^2    (Take the square root of both sides)

r ≈ 4.88726409338

r ≈ 5 inches.

Step-by-step explanation:

No of students work during day shift = 85

No of students work during night shift = 43

No of students working both shift = 28

So first we will divide 28 by 2 = 14

Then it means there were 14 students working in day shift and 14 students working in night shift

Total number of students work during day shift = 85 + 14 = 99

Answer:

11x-y

Step-by-step explanation:

You add 8x+3x and get 11x then you put the equation together

11x-y

HOPE THIS HELPS!!!

Answer:

QS + QR > RS

QR + RS > QS

RS + QS > QR

Step-by-step explanation:

JUST TOOK THE TEST

The complete Triangle Inequality is

The triangle inequality theorem defines the relationship between a triangle's three sides. The total of the lengths of the two sides of any triangle is always greater than the length of the third side, according to this theorem. In other words, the shortest distance between two unique points is always a straight line, according to this theorem.

According to Triangle Inequality " the sum of two side of the triangle is greater than the third side of Triangle."

Then, applying Triangle Inequality

QS + QR > RS

QR + RS > QS

RS + QS > QR

Learn more about Triangle Inequality here:

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To determine the sample size needed for a 99% confidence interval with a maximum width of .18 for a coin flip experiment, we must rely upon statistical principles such as the law of large numbers and the relationship between sample size and confidence interval width. Although we cannot give a specific number without more details, it is generally true that a larger sample size (i.e., more coin flips) results in a narrower confidence interval.

Your question pertains to finding the necessary sample size for a particular width of a confidence interval in a coin-flip experiment. A confidence interval represents the range where we are certain that the parameter, in this case, the probability of getting a head, lies to a certain degree, say 99%. Narrowing down this interval or making it smaller would require a larger number of coin flips or trials. The probable outcome of our experiment does indeed align with the theoretical probability when a large number of trials is conducted, which is also known as the law of large numbers.

The calculation of the size of a confidence interval involves standard deviation, confidence level (z-score) and sample size. By adjusting these parameters, we can alter the size of a confidence interval. For example, a 90% confidence interval would be smaller compared to a 95% interval due to the decreased degree of certainty. However, without exact numbers we cannot directly calculate how many flips are required for a 99% confidence interval of a certain width.

As a general rule of thumb, when conducting confidence interval tests, it would be safe to suggest that a larger sample size (which for a coin flip experiment would mean more coin flips) will result in a narrower confidence interval. Therefore, to achieve a 99% confidence interval of width at most .18, one would need net a large number of trials, or flips.

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Answer:

The expression is not factorable with rational numbers...

Step-by-step explanation:

Answer:

y = 6x-4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

We know the slope is 6 and the y intercept is -4

y = 6x + -4

y = 6x-4

Slope-intercept form: y = mx + b (m = slope and b = y-intercept)

Slope (m) = 6

y-intercept (b) = -4

Put into its final form.

y = 6x - 4

Best of Luck!

Answer:

2.4 or 2 2/5

Step-by-step explanation:

When you multiply 12/15 and 3 you get 2.4 or 2 2/5

Answer:

Exact form: 12/5

Decimal form: 2.4

Mixed number form: 2 2/5

Step-by-step explanation:

You multiply 12 by 3, and 15 by 1, then simplify your answer.

Answer:

Domain is where the function is defined.  In other words, all valid values of x that allows us to find y.

Range is values of y for the function.

Step-by-step explanation:

Here is the example of function [tex]y = \sqrt{x}[/tex], so domin is between 0 and positive infinity.  x cannot be negative.

The range is from 0 (because that's the lowest value of y) to positive infinity

Answer:

all nonzero real numbers for both of them

Step-by-step explanation:

e2021

Given:

Given that the length of VX is 15.

The length of WX is 7.

We need to determine the altitude UX of the given triangle.

Altitude UX:

The value of the altitude UX can be determined using the altitude rule theorem.

Applying the theorem, we have;

[tex]\frac{left}{altitude}=\frac{altitude}{right}[/tex]

Substituting left = UX, altitude = VX and right = VW in the above formula, we get;

[tex]\frac{UX}{VX}=\frac{VX}{XW}[/tex]

Substituting the values, we get;

[tex]\frac{UX}{15}=\frac{15}{7}[/tex]

Multiplying both sides of the equation by 15, we have;

[tex]UX=\frac{15 \times 15}{7}[/tex]

[tex]UX=\frac{225}{7}[/tex]

[tex]UX=32.14[/tex]

Thus, the length of UX is 32.14 units.

Answer: Its 32.14

Step-by-step explanation:

Answer:

3/5 then 11/5

Step-by-step explanation:

These symbols "I  I" represent absolute values.

11/5 equals to 2 1/5

3/5 is less than 2 1/5

Answer:

There are 3 equivalent fractions 28 /30, 42/45,56/6

Answer:

B. It has two faces that are decagons.

D. It has 20 edges.

E. It has 20 vertices.

Answer:b,d and e

Step-by-step explanation:

Answer:

a) The null hypothesis is

H₀: μ₀ = 3 inches

And the alternative hypothesis is

Hₐ: μ₀ ≠ 3 inches

b) Check Explanation.

c) The $3000 is obviously the cost of a type I error.

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and is always about the absence of significant difference between two proportions being compared. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup. It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to verify that the mean diameter produced by the machine is really off-target.

Note that, that target is 3 inches.

Hence, the null hypothesis will be that that there is no difference between the mean diameter of the 100 cylinders sampled and the target of 3 inches.

And the alternative hypothesis will confirm the concerns of the technical staff that there is a significant difference between the mean diameter of the 100 cylinders sampled and the target diameter of 3 inches. That is, the mean diameter is off-target.

Mathematically,

The null hypothesis is

H₀: μ₀ = 3 inches

And the alternative hypothesis is

Hₐ: μ₀ ≠ 3 inches

b) A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true. It involves saying there is significant evidence to show that the mean diameter of the sampled cylinders is indeed different from the targeted 3 in. (that is, the mean diameter of sampled cylinders is off-target), so they try to fix the issue when in reality, there is actually no significant difference between the mean diameter of sampled cylinders and the targeted 3 inches.

While a type II error involves failing to reject the null hypothesis when in reality it should have been rejected.

It entails not rejecting the null hypothesis and making conclusions based on the null hypothesis, when in reality, the alternative hypothesis should have been accepted together with its conclusion.

In this one the firm would conclude that they do not need to change anything as there is no significant difference between the mean diameter of the sampled cylinders and the targeted 3 inches, when in reality, there is a significant difference between the mean diameter of the sampled cylinders and the targeted 3 inches diameter.

c) The $3000 is obviously the cost of a type I error.

This is because the type I error is the one that involves tryin to fix the problem that did not even exist in reality.

Hope this Helps!!!

Answer:

Step-by-step explanation:

An Automobile Parts supplier owns a machine that produces a cylindrical engine part. The part is supposed to have an outside diameter of 3 inches in order for customers requirements to be met.

Lately, the company has been producing cylindrical engine parts with diameters that are either < 3inches or > 3inches. Technical staff feel that the mean diameter produced by the machine, from a random sample of 100 engine parts is not equal to 3 inches. The parts supplier wishes to set up a hypothesis test so that the problem-solving team can swing into action if or when the Null Hypothesis is rejected.

The null hypothesis is:

100 Cylindrical Engine Parts have a mean diameter = 3 inches

The alternative hypothesis is:

100 Cylindrical Engine Parts have a mean diameter that is NOT equal to 3 inches

[You can input the "not equal to" sign]

If the null hypothesis is rejected after statistical procedures, the supplier will proceed to employ the services of the problem-solving team!

Answer:

0.13% probability that this selected sample has an average thickness greater than 53

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, we have that:

[tex]\mu = 50, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]

What is the probability that this selected sample has an average thickness greater than 53?

This is 1 subtracted by the pvalue of Z when X = 53. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{53 - 50}{1}[/tex]

[tex]Z = 3[/tex]

[tex]Z = 3[/tex] has a pvalue of 0.9987

1 - 0.9987 = 0.0013

0.13% probability that this selected sample has an average thickness greater than 53

Answer:

59/10

Step-by-step explanation:

5+9/10

50/10 + 9/10

=59/10

Answer:

it 59/10

Step-by-step explanation:

Answer:

Part a

Null hypothesis: [tex]\mu =30[/tex]

Part b

Alternative hypothesis: [tex]\mu \neq 30[/tex]

Part c

Alternative hypothesis: [tex]\mu > 30[/tex]

Part d

Alternative hypothesis: [tex]\mu < 30[/tex]

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

For this case we want to test if the true mean is equal to 30 or no.

Part a

Null hypothesis: [tex]\mu =30[/tex]

Part b

Alternative hypothesis: [tex]\mu \neq 30[/tex]

Part c

Alternative hypothesis: [tex]\mu > 30[/tex]

Part d

Alternative hypothesis: [tex]\mu < 30[/tex]

The area of a rectangle combined with a semi-circle can be found by adding the rectangular area calculated via Length x Width to the semi-circular area calculated by 0.5 x π x r². The total area in this case would be approximately 5981.75 m².

The area of a field that is shaped like a rectangle with a semi-circle at one end can be found by summing the area of the rectangle and the area of the semi-circle. The area of a rectangle is given by the formula Length x Width. So in this instance, the rectangle's area would be 100m x 50m = 5000 m². The area of a semi-circle is given by the formula 0.5 x π x r², where r is the radius of the semi-circle. Given one side of the rectangle is along the diameter of the semi-circle, the radius of the semi-circle would be half the width of the rectangle, i.e., 25m. So the area of the semi-circle would be 0.5 x π x 25m² = 0.5 x 3.1416 x 625 = 981.75 m² approximately.  Therefore, the total area of the field would be 5000 m² + 981.75 m² which is 5981.75 m² approximately.

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Answer:

So we use the t-distribution to compute a confidence interval for the average age of people using online dating services

Step-by-step explanation:

Confidence interval for a mean.

We have to decide between the t-distribution and the z-distribution.

T-distribution: We use the sample standard deviation.

Z-distribution: We use the population standard deviation.

In this problem:

The average age of those that were using online dating services was 35 years old with a sample standard deviation of 12 years.

So we use the t-distribution to compute a confidence interval for the average age of people using online dating services

Answer:

The p-value should be smaller than 0.05.

Step-by-step explanation:

We know that the 95% confidence interval for the difference of means is (5.6, 10.2). As the lower bound is larger than 0, we are 95% confident that the reduction program had had a effect in the blood pressure level.

Then, as the program had a significant effect in the blood pressure level, we know that the null hypothesis (that states that the blood pressure levels would no change significantly) is then rejected.

If the significance level is 0.05, according to the confidence of the interval, to reject the null hypothesis, the p-value had to be lower than the significance level. In conclusion, the p-value should be lower than 0.05.

Answer:

Step-by-step explanation:

Answer:

The Answer is B.

Step-by-step explanation:

I took the test on Edg 2021 and got it right the first time.

Answer:

Step-by-step explanation:

You can use the simple one.

20*0.15*n year= answer

answer+20

or Compound

20*0.15 to de power of the year(s)

Based on the converse of the Corresponding Angles Theorem, if ∠8 ≅ ∠16, then the lines that must be parallel are: A) r and s.

What is the converse of corresponding angles theorem?

If two lines are cut by a transversal, and the corresponding angles are congruent, then the lines are parallel, which is the converse of the Corresponding Angles Theorem.

In the image below, angles 8 and 16 are said to be congruent to each other, and both lie on lines r and s.

Therefore, based on the converse of the Corresponding Angles Theorem, lines r and s must be parallel (option A).

Answer:

b) 74

The sample size that needs to be taken if the desired margin of error is 5 or less is 74

Step-by-step explanation:

Explanation:-

Given population variance σ² = 484

                                            σ = √484

                                            σ = 22

The level of significance ∝=0.95

The z-score of 0.95 level of significance = 1.96

Given Margin of error = 5

we know that the margin of error is determined by

[tex]M.E = \frac{Z_{\alpha }S.D }{\sqrt{n} }[/tex]

cross multiplication, we get

[tex]\sqrt{n} = \frac{Z_{\alpha }S.D }{M.E}[/tex]

[tex]\sqrt{n} = \frac{1.96 X22 }{5} = 8.624[/tex]

Squaring on both sides, we get

n = (8.624) ²

n = 74.37 ≅74

Conclusion:-

The sample size that needs to be taken if the desired margin of error is 5 or less is 74

Answer:

C

Step-by-step explanation:

If the line is parallel that means 1.2 has to be the same. And passing through (5,0) means a plus five.

Answer:

9/35

Step-by-step explanation:

-1/7 ÷ -5/9

Copy dot flip

-1/7 * -9/5

Multiply the numerators

-1*-9 = 9

Multiply the denominators

7*5 = 35

9/35

Step-by-step explanation:

[tex]\frac{-\frac{1}{7} }{-\frac{5}{9} }[/tex]

Invert the fraction in the denominator and multiply it by the fraction in the numerator.

[tex](-\frac{1}{7} )(-\frac{9}{5} )\\\\\frac{9}{35}[/tex]