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3 years ago

15

Jenny has $2.40 deducted from her monthly allowance every time she forgets to do a chore. If she forgets three times in one mont

h, what will be the change in Jenny's total allowance?

1 answer:

Hunter-Best [27]3 years ago

7 0

Answer:

The difference would be $7.20

Step-by-step explanation:

Multiply $2.40 times 3

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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 the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 36 minus the quantity of y plus 1

Sphinxa [80]

Answer:

Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)

Step-by-step explanation:

Center at (-5,-1) because of the plus 5 added to the x and the plus 1 added to the y.

a(squared)=36 which means a=6 and a=distance from center to vertices so add and subtract 6 from the x coordinate since this is a horizontal hyperbola, which is (1,-1), (-11,-1). From there you dont need to find the focus since there is only one option for this;

Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)

8 0

3 years ago

Read 2 more answers

-) You and a friend are at the store and want to buy some candy. You buy 7 bags of Gummy Bears and 3 bags of Chocolate and your

worty [1.4K]

24.00 hope this helps

6 0

3 years ago

Can somone help me with number 23 and 24

tangare [24]

23.

store price = 14 + 0.5(14)

store price = 21

customer price = 21 + 0.08(21)

customer price = 21 + 1.68

customer price = $22.68

24.

formula: A = P(1 + rt)

A = 140(1 + (0.03)(2))

A = 140(1.06)

A = 148.40

interest = 148.40 = 140

interest = $8.40

Hope this helps!! :)

7 0

4 years ago

Read 2 more answers

The bill for lunch was 24.50 mr smith add a 20% tip how much did mr smith pay

miss Akunina [59]

Answer:

Mr.Smith paid $29.4.

Step-by-step explanation:

Mr.Smith paid $24.5 plus additional 20% of $24.5, and to figure out the total amount that he paid, we need to know what is 20% of $24.50.

20% of $24.50 is:

$\frac{20}{100}*24.5=0.2*24.6=4.9$ .

Mr.Smith paid additional $4.9; therefore, the total amount he paid was

$24.5 + $4.9 = $29.4.

Mr. smith paid $29.4.

4 0

3 years ago