Simplify (2x - 5)(x + 3) = 0

A high school runs a survey asking students if they participate in sports. The results are found below. Run an independence test

Sveta_85 [38]

Answer:

It can be concluded that participation in sports is dependent on grade level.

Step-by-step explanation:

In this case a Chi-square independence test for the data is to be performed at α = 0.01.

The hypothesis can be defined as follows:

H₀: The participation in sports is independent of grade level.

Hₐ: The participation in sports is dependent of grade level.

The data provided is:

Freshmen Sophomores Juniors Seniors

Yes 75 88 55 42

No 30 28 38 40

The formula to compute the expected frequencies is:

$E_{i}=\frac{i^{th}\ \text{Row Total}\ \times\ i^{th}\ \text{Column Total}}{N}$

The Chi-square statistic is:

$\chi^{2}=\sum {\frac{(O_{i}-E_{i})^{2}}{E_{i}}}$

Consider the Excel file attached below.

The value of Chi-square statistic is 16.244.

The degrees of freedom of the test are:

$\text{df}=(r-1)(c-1)$

$=(4-1)(2-1)\\=3\times 1\\=3$

Compute the p-value of the test as follows:

$p-value=P(\chi^{2}_{df}$

$=P(\chi^{2}_{3}$

*Use a Chi-square table.

p-value = 0.001 < α = 0.01

The null hypothesis will be rejected at 1% level of significance.

Thus, it can be concluded that participation in sports is dependent on grade level.

4 0

4 years ago

Find the volume v of the described solid s. a right circular cone with height 7h and base radius 3r

jarptica [38.1K]

Answer in cm if you need something else state it in the question.

r = 3 cm
h = 7 cm
s = 7.61577 cm
V = 65.9734 cm³
L = 71.777 cm²
B = 28.2743 cm²
A = 100.051 cm²

Agenda:

r = radius
h = height
s = slant height
V = volume
L = lateral surface area
B = base surface area
A = total surface area
π = pi = 3.14159
√ = square root

Formula: Volume of a cone: V = (1/3)πr²h

7 0

4 years ago

-the equations x-y=-14 and -x-y=14 what is the number of solutions? A.) no solutions B.) infinitely many solutions C.) one solut

Yuki888 [10]

Answer:

The answer is C one solution

Step-by-step explanation:

x-y=-14

-y=-x-14 bring x to the other side

y=x+14 divide everything by -1

-x-y=14

-y=x+14 bring x to the other side

y=-x-14 divide everything by -1

6 0

3 years ago

A jug holds 5 gallons of water. If a glass holds 4 ounces of water, how many glasses can be drawn from the water jug?

MariettaO [177]

Hey You!

1 gallon = 16 cups.

5 gallons = 80 cups.

80 glasses can be filled from the jug.

4 0

3 years ago

The mean consumption of bottled water by a person in the United States is 28.5 gallons per year. You believe that a person consu

Over [174]

Answer:

$t=\frac{27.8-28.5}{\frac{4.1}{\sqrt{100}}}=-1.707$

$p_v =P(t_{99}$

If we compare the p value with a significance level for example $\alpha=0.1$ we see that $p_v$ so we can conclude that we reject the null hypothesis, so there is not enough evidence to conclude that the mean for the consumption is less than 28.5 gallons at 0.1 of significance, so we can reject the claim that person consume more than 28.5 gallons.

Step-by-step explanation:

Data given and notation

$\bar X=27.8$ represent the mean for the account balances of a credit company

$s=4.1$ represent the population standard deviation for the sample

$n=1000$ sample size

$\mu_o =28.5$ represent the value that we want to test

$\alpha=0.1$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean for the person consume is more than 28.5 gallons, the system of hypothesis would be:

Null hypothesis: $\mu \geq 28.5$

Alternative hypothesis: $\mu < 28.5$

We don't know the population deviation, so for this case we can use the t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{27.8-28.5}{\frac{4.1}{\sqrt{100}}}=-1.707$

Calculate the P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=100-1=99$

Since is a one-side lower test the p value would be:

$p_v =P(t_{99}$

In Excel we can use the following formula to find the p value "=T.DIST(-1.707,99)"

Conclusion

If we compare the p value with a significance level for example $\alpha=0.1$ we see that $p_v$ so we can conclude that we reject the null hypothesis, so there is not enough evidence to conclude that the mean for the consumption is less than 28.5 gallons at 0.1 of significance, so we can reject the claim that person consume more than 28.5 gallons.

5 0

4 years ago