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ind the value of the test statistic z using z equals StartFraction ModifyingAbove p with caret minus p Over StartRoot StartFraction pq Over n EndFraction EndRoot EndFractionz= p−p pq n. The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%). The sample statistics from one experiment include 530530 peas with 139139 of them having yellow pods.

Answers

Answer 1

Answer:

Answer:

$z=\frac{0.262 -0.25}{\sqrt{(0.25(1-0.25))/(530)}}=0.638$

Step-by-step explanation:

Data given and notation

n=530 represent the random sample taken

X=139 represent the yellow pods in the random sample

$\hat p=(139)/(530)=0.262$ estimated proportion of yellow pods

$p_o=0.25$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.25 or 25%:

Null hypothesis: $p=0.25$

Alternative hypothesis: $p \neq 0.25$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.262 -0.25}{\sqrt{(0.25(1-0.25))/(530)}}=0.638$

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I NEED HELP, PLEASE!!Two numbers have a distance of 6 units from 0 on a number line. The numbers can be graphed on the number line as points A and B.

Drag and drop the labels to the correct positions on the number line.

Answers

Answer:

You have to put A on -6 and b on 6.

Step-by-step explanation:

IN order to solve tis you just have to take one of the markers, lets say A and move it 6 units to the left all the way to -6, then you just have to move the B marker 6 units to the right from 0 all the way to the 6, that is how you get the two numbers that have a distanceof 6 units from 0 on the number line.

Answer:

See attached image.

Step-by-step explanation:

Start at 0 and count to the right. When you get to 6, place EITHER marker on the point. It doesn't look like it matters whether you use A or B.

Start at 0 and count to the left. When you get to 6, place the other marker on the point.

PLZ SHOW STEP BY STEP EXPLANATION FOR BRAINLIEST Three monkeys met for tea in their favourite café, taking off their hats as they arrived. When they left, they each put on one of the hats at random.

What is the probability that they all left wearing the wrong hat?

Answers

Answer:

2/6 or 1/3

(Please vote me Brainliest if this helped!)

Step-by-step explanation:

Call monkeys A, B and C and hats 1, 2 and 3

You have :

A1, B2, C3 (all have the right hat)
A2, B1, C3
And so on.

Now, a little more advanced way to solve this is to count in your head. Each outcome gives you a permutation of {1, 2, 3} so there are 3! = 6 Outcomes. Now, if they all wear the wrong hat, you have two choices for the hat of A and then only one choices for B and C. For instance you can choose A2 or A3. If you choose A2 then you must choose B3 and C1.

A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. Group members took a random sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged overnight and the number of hours of use before needing to be recharged was recorded. Company A toothbrushes operated for an average of 119.7 hours with a standard deviation of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a standard deviation of 1.72 hours.1. which of the following statements is true?A. This is a one tailed test of two dependent samplesB. This is a two tailed test of two independent samplesC. This is a one tailed test of two independent samplesD. These samples are matchedE. None of the above

Answers

Answer: Lyrics B

Step-by-step explanation:

The investigation about the operating time of cordless toothbrushes is in first place associated to two tails experiment since investigation call for evalution of values under and above any given value (mean value). On the other side investigation of two different manufactures implies totally independent samples, unless these two companies have a commercial relationship which is not express in the problem ststement. Therefore the answer is lyrics B

How do you do these two questions?

Answers

Answer:

(a) ⅛ tan⁻¹(¼)

(b) sec x − ln│csc x + cot x│+ C

Step-by-step explanation:

(a) ∫₀¹ x / (16 + x⁴) dx

∫₀¹ (x/16) / (1 + (x⁴/16)) dx

⅛ ∫₀¹ (x/2) / (1 + (x²/4)²) dx

If tan u = x²/4, then sec²u du = x/2 dx

⅛ ∫ sec²u / (1 + tan²u) du

⅛ ∫ du

⅛ u + C

⅛ tan⁻¹(x²/4) + C

Evaluate from x=0 to x=1.

⅛ tan⁻¹(1²/4) − ⅛ tan⁻¹(0²/4)

⅛ tan⁻¹(¼)

(b) ∫ (sec³x / tan x) dx

Multiply by cos x / cos x.

∫ (sec²x / sin x) dx

Pythagorean identity.

∫ ((tan²x + 1) / sin x) dx

Divide.

∫ (tan x sec x + csc x) dx

Split the integral

∫ tan x sec x dx + ∫ csc x dx

Multiply second integral by (csc x + cot x) / (csc x + cot x).

∫ tan x sec x dx + ∫ csc x (csc x + cot x) / (csc x + cot x) dx

Integrate.

sec x − ln│csc x + cot x│+ C

Answer:

(a) Solution : 1/8 cot⁻¹(4) or 1/8 tan⁻¹(¼) (either works)

(b) Solution : tan(x)/sin(x) + In | tan(x/2) | + C

Step-by-step explanation:

(a) We have the integral (x/16 + x⁴)dx on the interval [0 to 1].

For the integrand x/6 + x⁴, simply pose u = x², and du = 2xdx, and substitute:

1/2 ∫ (1/u² + 16)du

'Now pose u as 4v, and substitute though integral substitution. First remember that we have to factor 16 from the denominator, to get 1/2 ∫ 1/(16(u²/16 + 1))' :

∫ 1/4(v² + 1)dv

'Use the common integral ∫ (1/v² + 1)dv = arctan(v), and substitute back v = u/4 to get our solution' :

1/4arctan(u/4) + C

=> Solution : 1/8 cot⁻¹(4) or 1/8 tan⁻¹(¼)

(b) We have the integral ∫ sec³(x)/tan(x)dx, which we are asked to evaluate. Let's start by substitution tan(x) as sin(x)/cos(x), if you remember this property. And sec(x) = 1/cos(x) :

∫ (1/cos(x))³/(sin(x)/cos(x))dx

If we cancel out certain parts we receive the simplified expression:

∫ 1/cos²(x)sin(x)dx

Remember that sec(x) = 1/cos(x):

∫ sec²(x)/sin(x)dx

Now let's start out integration. It would be as follows:

$\mathrm{Let:u=(1)/(\sin \left(x\right)),\:v'=\sec ^2\left(x\right)}\n=> (\tan \left(x\right))/(\sin \left(x\right))-\int \:-\cot \left(x\right)\csc \left(x\right)\tan \left(x\right)dx\n\n\int \:-\cot \left(x\right)\csc \left(x\right)\tan \left(x\right)dx=-\ln \left|\tan \left((x)/(2)\right)\right|\n=> (\tan \left(x\right))/(\sin \left(x\right))-\left(-\ln \left|\tan \left((x)/(2)\right)\right|\right)\n$

$=> (\tan \left(x\right))/(\sin \left(x\right))+\ln \left|\tan \left((x)/(2)\right)\right|\n\n=> (\tan \left(x\right))/(\sin \left(x\right))+\ln \left|\tan \left((x)/(2)\right)\right|+C$