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2 years ago

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The following hypotheses are given. H0 : σ1² = σ2² H1 : σ1² ≠ σ2² A random sample of eight observations from the first populatio

n resulted in a standard deviation of 10. A random sample of six observations from the second population resulted in a standard deviation of 7.
1. State the decision rule for 0.02 significance level. (Round your answer to 1 decimal place.) Reject H0 if F >
2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)
3. At the 0.02 significance level, is there a difference in the variation of the two populations?
__________H0. There is ______ in the variations of the two populations

2 answers:

Lunna [17]2 years ago

8 0

Answer:

Step-by-step explanation:

From the question; for 0.02 level and $n_1 -1 = 7$ ; $n_2 -1 = 5$ ; degree of freedom.

The critical value (F) = 0.1340 and 10.4555

Decision rule: reject $H_o$ if test statistic $F>10.5$ ( to one decimal place) or $F$ ( to on decimal place)

Test statistic:

$F = (\frac{s_1}{s_2})^2 \\ \\ = (\frac{10}{7})^2 \\ \\$

= 2.0408

= 2.04 (to two decimal place)

As test statistic does not fall into critical region we can not reject null hypothesis.

Conclusion:

<u>Accept </u> $H_o$ .There is <u>significant</u> variations of the two population.

stiks02 [169]2 years ago

6 0

Answer:

Step-by-step explanation:

This is a two tailed test for comparison of two variances at 2% significance level

$n_1 = 8: n_2 =6\\s_1 =10: s_2 = 7$

deg of freedom = 7

F statistic = $\frac{s_1^2}{s_2^2} =\frac{100}{49} \\=2.041$

p value = 0.4496

1. State the decision rule for 0.02 significance level. (Round your answer to 1 decimal place.) Reject H0 if F >10.4555

2.F=2.041

3. _Accept_________H0. There is __no significant____ in the variations of the two populations

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Answer:

$Sum = -81$

Step-by-step explanation:

See the comment for complete question.

Given

$c = 36$ ----- Constant

No coefficient of x^2

Required:

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Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

$x^2 + ax + 36 = 0$

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

$x = -\alpha$ and $x = -\beta$

Using the above roots, the equation can be represented as:

$(x + \alpha)(x + \beta) = 0$

Open brackets

$x^2 + (\alpha + \beta)x + \alpha \beta = 0$

To compare the above equation to $x^2 + ax + 36 = 0$ , we have:

$a = \alpha + \beta$

$\alpha \beta = 36$

Where: $\alpha, \beta$ and $\alpha \ne \beta$

The values of $\alpha$ and $\beta$ that satisfy $\alpha \beta = 36$ are:

$\alpha = -1$ and $\beta = -36$

$\alpha = -2$ and $\beta = -18$

$\alpha = -3$ and $\beta = -12$

$\alpha = -4$ and $\beta = -9$

So, the possible values of a are:

$a = \alpha + \beta$

When $\alpha = -1$ and $\beta = -36$

$a = -1 - 36 = -37$

When $\alpha = -2$ and $\beta = -18$

$a = -2 - 18 = -20$

When $\alpha = -3$ and $\beta = -12$

$a = -3 - 12 = -15$

When $\alpha = -4$ and $\beta = -9$

$a = -4 - 9 = -13$

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

$Sum = -37 -20 -15 - 9$

$Sum = -81$

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Step-by-step explanation:

To state 1/50 in percent, divide 1 by 50, then multiply by 100

=( 1 ÷ 50) x 100

= 0.02 x 100

= 2%

I hope this helps, please mark as brainliest.

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2 years ago

F (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20 Three roots of this polynomial function are −1, 1, and 3 + i. Which of the following d

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In equilateral ∆ABC with side a, the perpendicular to side AB at point B intersects extension of median AM in point P. What is t

Sergeeva-Olga [200]

Answer:

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Step-by-step explanation:

Given: ΔABC is equilateral and AB = a

The diagram is given below :

AM is a median , PB ⊥ AB , PM = b

Now, by using properties of equilateral triangle, median is perpendicular bisector and each angle is of 60°.

We get, ∠AMB = 90°. So, by linear pair ∠AMB + ∠PMB = 180° ⇒ ∠PMB = 90°. Also, ∠ABC = 60° and ∠ABP = 90° (given) So, ∠PBM = 30°

Since, AM is perpendicular bisector of BC. So,

$MB = \frac{a}{2}$

Now in ΔAMB , By using Pythagoras theorem

$AB^{2}=AM^{2}+MB^{2}\\AM^{2}=AB^{2}-MB^{2}\\AM^{2}=a^{2}-(\frac{a}{2})^{2}\\AM=\frac{\sqrt{3}\cdot a}{2}$

Now, in ΔBMP :

$sin\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\sin\thinspace 30^{o}=\frac{\text{MB}}{\text{PB}}\\\\PB=\frac{\text{MB}}{\text{sin 30}}\\\\PB=\frac{\frac{a}{2}}{\frac{1}{2}}\implies PB = a\\\\tan\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Base}}\\\\tan\thinspace 30^{o}=\frac{\text{MB}}{\text{PM}}\\\\PM=\frac{\text{MB}}{\text{tan 30}}\\\\PM=\frac{\frac{a}{2}}{\frac{1}{\sqrt3}}\implies PM=b= \frac{\sqrt{3}\cdot a}{2}$

Perimeter of ABM = AB + PB + PM + AM

$\text{Perimeter = }a+a+b+ \frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a + \frac{\sqrt{3}\cdot a}{2} +\frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a +\sqrt{3}\cdot a\\\\=(2+\sqrt3})\cdot a$

Hence, Perimeter of ΔABP = (2 + √3)·a units

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1 year ago

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Westkost [7]

Answer:

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Step-by-step explanation:

The total lenght of the pool is 25.

Since both of them standing 3 m from one side of the pool, then, the total distance both need to cover is $25-3$ m= 22 m.

Assume that the distance traveled by Ario before Miguel start to swin is $x$ . That means, the remaining distance to Ario (to cover the total size of the pool) is $22-x$ .

Then, in acoordance to the problem, the ratio between these two distances must be equal to 1/4.

That is,

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2 years ago