Biologists were studying the proportions of cats that had spotted markings on their fur in two populations of cats, C and F. An independent random sample of cats was taken from each population, and the difference between the sample proportions of cats with the spotted markings (C minus F) was 0.62. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being that the population proportions are not equal. The p-value of the test was 0.01.
Which of the following is the correct interpretation of the p-value?

If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at least 0.62 or at most −0.62 is 0.01.
A

If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at least 0.62 is 0.01.
B

If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at most −0.62
is 0.01.
C

If the difference in proportions of cats with spotted markings between the two populations is actually 0.62, the probability of observing that difference is 0.01.
D

If the difference in proportions of cats with spotted markings between the two populations is actually 0.01, the probability of observing that difference is 0.62.
E

The probability of observing the given sample difference of at least 0.62 is 0.01 when the proportions of spotted marking in all cats are the same.  Option B is correct.

It is the probability that tells how likely the data comes under the Null hypothesis of the statistical test.

The calculated p-value = 0.01.

The Null hypothesis is:   "Population Proportions are not equal"

The sample difference is 0.62

According to the definition of the p-value.

If the population proportions are the same, the probability of obtaining a sample difference of at least 0.62 is 0.01.

Since this is only followed by statement B.

Therefore, the probability of observing the given sample difference of at least 0.62 is 0.01 when the proportions of spotted marking in all cats are the same.

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If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at least 0.62 is 0.01.

Step-by-step explanation:

p-value is the probability of observing a result which is at least as extreme as we calculated in our actual workings, assuming the Null hypothesis to be true.

The calculate p-value is 0.01. In the question statement we are given that the alternate hypothesis is:

"Population Proportions are not equal"

Since, Null and Alternate Hypothesis are negations of each other, the Null Hypothesis would be:

"Population Proportions are equal"

We assume the null hypothesis to be true, perform the tests on the sample and obtain a result.

The results we obtained is:

The sample difference is 0.62

Fitting all this data, in the definition of p value tell us that:

The probability of obtaining a sample difference of atleast 0.62 is 0.01, if the population proportions are same.

This matches with the option B. Therefore, the correct answer is:

If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at least 0.62 is 0.01.

correct choice is a

step-by-step explanation:

the equation of the line passing through the points and is

thus, the equation of the line that passes through the points (0, -6) and (-3, 0) is

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9