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Dmitry_Shevchenko [17]
2 years ago
12

Question

Mathematics
1 answer:
Bingel [31]2 years ago
3 0

Answer:

u should put his is English and then translate it to read it

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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
Jasmine took a cab Home form her office the cab charged a flat free of 4$ plus $2 per mile jasmine paid $33 for the trip how man
Lostsunrise [7]
33 - 4 = 29.

29 / 2 = 14.5

She traveled 14.5 miles in the cab.

Please mark Brainliest if it helped!

3 0
3 years ago
Read 2 more answers
A department store buys 300 shirts for a total cost of $7,200 and sells them for $30 each. Find the percent markup.
Novosadov [1.4K]

Answer:

80%

Step-by-step explanation:

because 7200 / 300 equals 24 and 24 / 30 equals .8 so its 80% and if you want to check the answer you take 30 * .8 OR 80% and it gives you 24

3 0
3 years ago
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Please answer this I will give u​
satela [25.4K]

Answer:

Step-by-step explanation:

The 3 angles must add up to 180. So

6x + 4x + 2x = 180

12x = 180

x = 15

Plug this into all the angles and you have your answers

5 0
3 years ago
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Find value of X. Please show steps:)
Viefleur [7K]
10 degrees is in a 90 degree angle 
90-10 =80
use sin 
sin(80)=9/x
get x alone
x=9/sin(80)

4 0
3 years ago
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