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2 years ago

Even More FREEEEEEEE points

Mathematics

2 answers:

avanturin [10]2 years ago

8 0

Answer:

YASSS

Step-by-step explanation:

dont need oneee

jek_recluse [69]2 years ago

7 0

Answer:

TYSM!!!!!!!!!!!!!!!!

Step-by-step explanation:

THX!!!THX!!!THX!!!!!!!u r so awesome!!!!!!!!!!!!!!!!!!TYSM!!!!!!!!!

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A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that

mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = <u><em>probability of obtaining head.</em></u>

So, Null Hypothesis, $H_0$ : p = 0.5

Alternate Hypothesis, $H_A$ : p $\neq$ 0.5

(a) The significance level of the test which is represented by $\alpha$ is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

P(Type I error) = $\alpha$

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

$\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}$ = $\alpha$

$(1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})$ = $\alpha$

$\alpha$ = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

$1-\beta$ = $\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}$

$1-\beta$ = $(1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})$

$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

3 0

3 years ago

Find d<br><br> a * a * a = 216<br> a * b * c = 96<br> b * c = 52<br> a + b + c = d

Slav-nsk [51]

$a\cdot a\cdot a=216\\\\a^3=216\to a=\sqrt[3]{216}\\\\\boxed{a=6}\\\\\text{Substitute}\ b\cdot c=52\ \text{to the second expression}\ a\cdot b\cdot c=96:\\\\abc96\ \wedge\ bc=52\to a(52)=96\qquad\text{divide both sides by 52}\\\\a=\dfrac{96}{52}\to a=\dfrac{24}{13}\neq6$

a = 6 and a = 24/13 FALSE!!!

<h3>Answer: NO SOLUTION.</h3>

3 0

3 years ago

Will mark brainliest if right!!!!!!

77julia77 [94]

Answer:

sorry if wrong put b as the answer

4 0

2 years ago

Which statement is true?

seropon [69]

Answer: C. A line that rises from left to right has a positive slope.

Step-by-step explanation: A. has a slope of 0, B. has an undefined slope, and D. is supposed to go left to right not right to left.

6 0

3 years ago

How many 0.5cm x 0.5 cm x 0.5cm cubes are needed to completely fill the rectangular prism measuring 4 cm x 3 cm x 3cm?mp

Juliette [100K]

Answer:

288

Step-by-step explanation:

The volume of the cube is 0.5^3 = 0.125, and the volume of the rectangular prism is 4*3*3 = 36.

Now, you just divide 36 by 0.125, which is 288.

I hope this helped.

6 0

2 years ago