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Karo-lina-s [1.5K]
3 years ago
12

Describe how to write the null and alternative hypotheses based on a claim. Provide at least one example to clarify your explana

tion.
Mathematics
1 answer:
Umnica [9.8K]3 years ago
7 0

Answer:

Step-by-step explanation:

The null and alternative hypothesis are usually used in hypothesis testing to present the claim being tested as give in terms of the mean or proportion :

Given that the mean score of high school students is 10 ; using a sample of 50 students, a mean of 8 was obtained ; we could want to test the claim that the mean score is less than 10.

Here; population mean, μ = 10 ; the claim is now that, μ < 10 based on what was observed about the sample.

H0 : μ = 10

H0 : μ < 10

If we wanted to test If the mean was greater than 10 ; then the sign is reversed

H0 : μ = 10

H0 : μ > 10

If we wanted to test If the score is just different from the mean score stated ; (it may be less than or greater than)

H0 : μ = 10

H0 : μ ≠ 10

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Aysha has 40 cubes in a bag.
marissa [1.9K]

Given:

Total number of cubes = 40

Red cubes = 18

Blue cubes = 13

Yellow cubes = 9

Aysha adds some more red cubes into the bag.

The probability now that she will take a red cube is 0.5.

To find:

The probability that she will take a yellow cube.

Solution:

Let Aysha adds x red cubes into the bag. Then,

Number of total cubes = 40+x

Number of red cubes = 18+x

Probability of getting a red cube is:

P(Red)=\dfrac{18+x}{40+x}

The probability now that she will take a red cube is 0.5. So,

\dfrac{18+x}{40+x}=0.5

18+x=0.5(40+x)

18+x=20+0.5x

x-0.5x=20-18

0.5x=2

Divide both sides by 0.5.

x=\dfrac{2}{0.5}

x=4

It means Aysha adds 4 more red cubes into the bag.

Now, the total number of cubes int he bag is:

40+4=44

Probability of getting a yellow cube is:

P(Yellow)=\dfrac{\text{Number of yellow cubes}}{\text{Total number of cubes}}

P(Yellow)=\dfrac{9}{44}

Therefore, the required probability is P(Yellow)=\dfrac{9}{44}.

8 0
2 years ago
Gene invested $400 at 4% interest compounded quarterly.<br> How much is in the account after 1 year?
Ivenika [448]

Answer:

$416.24

Step-by-step explanation:

4 0
3 years ago
A spinner has 10 ​equal-sized sections. Two of the sections are red.
hichkok12 [17]

Answer:

a. Probability of landing on red = \frac{1}{5}

b. <em>See Explanation</em>

Step-by-step explanation:

Given

A Spinner

Number of section = 10 (equal sized)

Number of red section = 2

Required

- Probability of landing on red

- Describe the probability in words

Calculating the probability of landing on red

The formula used in calculating probability is as follows

Probability = Number of required outcomes / Number of possible outcomes

In this case, the number of required outcomes is the number of red section.

Hence, number of required outcomes  = 2

And the number of possible outcomes is the total section of the spinner

Hence, Number of possible outcomes = 10

By Substitution

Probability of landing on red = \frac{2}{10}

Probability of landing on red = \frac{1}{5}

Describe the probability in words

From (a) above, we have that the probability of the spinner landing on color red is \frac{1}{5}

This means that, for every five times, you spin the spinner, it's likely that one of the outcomes will be red.

8 0
3 years ago
HELP!!!
Naddika [18.5K]

Check the picture below, so it reaches the maximum height at the vertex, let's check where that is

h(t)=64t-16t^2+0 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+64}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 64}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (64)^2}{4(-16)}\right)\implies \stackrel{maximum~height}{(2~~,~~\stackrel{\downarrow }{64})}

5 0
2 years ago
Minute Maid states that a bottle of juice contains 473 mL. Consumer groups are interested in determining if the bottles contain
olga2289 [7]

Answer:

Option C) The average contents of all bottles of juice in the population, which is 473 mL

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 473 mL

Sample mean, \bar{x} = 472 mL

Sample size, n = 30

Sample standard deviation, σ = 0.2

First, we design the null and the alternate hypothesis

H_{0}: \mu = 473\text{ mL}\\H_A: \mu < 473\text{ mLinches}

Representation of \mu

  • \mu is the population parameter that represents the population mean.

Thus, for the given situation \mu represents:

Option C) The average contents of all bottles of juice in the population, which is 473 mL

6 0
3 years ago
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