A car is 195 inches long. A truck is 85% longer than the car. How long is the truck?

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

If 1/2 cup of soup equals 120 milliliters, then how many milliliters are in 3 1/2 cups of soup?

pav-90 [236]

Ok. So since they give you that 1/2 cup of soup equals 120 milliliters it makes this very easy. So since we know 120milliliters=1/2 and that 3 1/2= 7 1/2s (please note that the 7 1/2s doesnt mean seven and 1/2 it means seven 1/2s) you just add 120 to itself 7 times getting an answer of 840. (please vote brainliest ^^)

8 0

3 years ago

2x-5) = 2(x-5) One Solution Infinitely Many Solutions No Solution 5x + 4) = 5(1-6) 5(x + 4) = 3(x-6) 4x - 2) = 4(x + 2) x + 2(x-

Gekata [30.6K]

9514 1404 393

Answer:

top down: ∞, 0, 1, 0, ∞

Step-by-step explanation:

The equation will have infinite solutions when the left side and right side simplify to the same expression. This is the case for the first and last expressions listed.

2(x -5) = 2(x -5) . . . . expressions are already identical

x +2(x -5) = 3(x -2) -4 ⇒ 3x -10 = 3x -10 . . . the same simplified expression

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The equation will have no solutions when the x-coefficients are the same, but there are different added constants.

5(x +4) = 5(x -6) ⇒ x +4 = x -6 . . . not true for any x

4(x -2) = 4(x +2) ⇒ x -2 = x +2 . . . not true for any x

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The equation will have one solution when coefficients of x are different.

5(x +4) = 3(x -6) ⇒ 2x = -38 ⇒ x = -19

4 0

3 years ago

In January, Jamie pays $2.00 for a tube of toothpaste.

mariarad [96]

Answer:

12% or 13% rounded

Step-by-step explanation:

.25 of 2.00 is .125 or 12% or 13% rounded

3 0

3 years ago

To which subset of real numbers does the number 1/5 belong

Travka [436]

1/5 is an expression that represents 1÷5= .2
Since the return decimal equivalent doesn't go on forever and has a finite end, this is a member of the rational number set.

4 0

3 years ago