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3 years ago

The figure is to be rotated 1/4 (90 degrees) turn about point P.

Mathematics

1 answer:

Mariulka [41]3 years ago

7 0

The answer is C. 7 units. just turn it to the position of 90 degrees.

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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

To make lemonade, you used one quart of water, one pint of lemon juice, and 9 ounces of your secret ingredient: honey. How much

WITCHER [35]

To solve this problem you must follow the proccedure shown below:

1. Amount of lemonade in pints:

1 quart of water=2 pints
1 pint of lemon
(9 ounces of honey)(0.0625 pints/1 ounce)=0.56 pints

Total in pints=2 pints+1 pint+0.56 pints
Total in pints=3.56 pints

2. Amount of lemonade in cups:

Total in cups=(3.56 pints)(2 cups/1 pint)
Total in cups=7.12 cups

3. Amount of lemonade in ounces:

Total in ounces=(7.12 cups)(8 ounces/1 cup)
Total in ounces=56.96 ounces

4 0

3 years ago

Find the slope and the y-intercept of the line y=9x-8

german

Answer:

the slope is 9 and the y-int. is -8

Step-by-step explanation:

4 0

3 years ago

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A property was assessed at 25% of value with a tax rate of $12 per hundred. if the taxes totaled $11,400, what was the value? 1

shusha [124]