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3 years ago

Could anybody help with this question? My teacher didn’t give a review so I’m not sure what to do. Any help is appreciated!

Mathematics

1 answer:

Allisa [31]3 years ago

8 0

Answer: 6

Step-by-step explanation: set the equations equal to each other then solve. plug that number into the equation for AB

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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 = probability of obtaining head.

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

Match each expression in the left column with the correct product in the right column.

lesya692 [45]

Answer:

-6

-6i

Step-by-step explanation:

1) √4 . √-3 . √-3

$\sqrt{4} = 2$

$\sqrt{-3} . \sqrt{-3} = (\sqrt{-3})^2$

$\sqrt{4} . (\sqrt{-3})^2 = 2 \times -3 =$ -6

2) √-4 . √-3 . √-3

$\sqrt{-4} = 2i$ .

Therefore, $\sqrt{-4} . \sqrt{-3} . \sqrt{-3} = 2. \sqrt{-1} \times -3 = 2i \times (-3) =$ - 6i

3) √4 . √3 . √-3

$\sqrt{4} = 2$

$\sqrt{3} . \sqrt{-3} = (\sqrt{3})^2 . \sqrt{-1}$

$\implies 2 \times 3i =$ 6i

4) √4 . √3 . √3

$\sqrt{4} = 2$

$\sqrt{3} . \sqrt{3} = (\sqrt{3})^2 = 3$

Therefore, √4 . √3 . √3 = 2 . 3 = 6

5 0

3 years ago

Write each ratio as a fraction in simplest form. 5. 48 : 76 6. 20 inches to 4 feet

Delicious77 [7]

Answer:

48:76 would be 48/76 which would reduce to 12/19.

20:4 would be 5/1 reduced or just 5.

3 0

2 years ago

Tell weather each pair is parallel, perpendicular, or neither: 3х + 2y = 5 Зу + 2x = -3

kakasveta [241]

None of them are parallel

8 0

2 years ago

Can someone please help me out

Paha777 [63]

Answer:

D. 20.

Step-by-step explanation:

-17 - -37 = 20.

These are all of the steps, to completely, get the correct answer to this question.

Hope this helps!!!

Kyle.

8 0

2 years ago