Six Less than four times a number is -70

The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar busi

eimsori [14]

Answer:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=4.2$ represent the sample mean

$s=1.4$ represent the sample standard deviation

n=16 represent the sample selected

$\alpha=0.05$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 3.6, the system of hypothesis would be:

Null hypothesis: $\mu = 3.6$

Alternative hypothesis: $\mu \neq 3.6$

If we analyze the size for the sample is < 30 and we know the population deviation so is better apply a 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:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Critical values

On this case since we have a bilateral test we need to critical values. We need to use the t distribution with $df=n-1=16-1=15$ degrees of freedom. The value for $\alpha=0.05$ and $\alpha/2=0.025$ so we need to find on the t distribution with 15 degrees of freedom two values that accumulates 0.025 of the ara on each tail. We can use the following excel codes:

"=T.INV(0.025,15)" "=T.INV(1-0.025,15)"

And we got $t_{crit}=\pm 2.131$

So the decision on this case would be:

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

Conclusion

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

3 0

4 years ago

Translate the sentence into an inequality.

lord [1]

Answer:

2(W - 5) ≤ -29

Step-by-step explanation:

"Twice the difference of a number and 5 is at most -29" can be expressed symbolically as follows:

2(W - 5) ≤ -29

Further explanations:

"the difference of a number and 5" is W - 5, and thus "Twice the difference of a number and 5" is 2(W - 5).

"x ≤ -29" states "x is at most -29."

7 0

3 years ago

The graph of the equation x^2+6x+y^2-16y=-9 is a circle. Choose True or False for each statement

BigorU [14]

Answer:

see the explanation

Step-by-step explanation:

we have

$x^2+6x+y^2-16y=-9$

Convert the equation of the circle in center radius form

Group terms that contain the same variable

$(x^2+6x)+(y^2-16y)=-9$

Complete the square twice. Remember to balance the equation by adding the same constants to each side

$(x^2+6x+9)+(y^2-16y+64)=-9+9+64$

$(x^2+6x+9)+(y^2-16y+64)=64$

Rewrite as perfect squares

$(x+3)^2+(y-8)^2=8^2$

The center of the circle is (-3,8)

The radius of the circle is 8 units

Verify each statement

A. The center of the circle is (3,-8).

False

The center of the circle is (-3,8)

B. The circle is tangent to the x-axis

True

The circle is tangent to x=5 and x=-11 and is tangent to y=0 and y=16

Remember that y=0 is the x-axis

C. The circle has a radius of 64

False

The radius of the circle is 8 units

7 0

3 years ago

81+ 3 = what help me pleasee

Slav-nsk [51]

84 Hope I Helped! ( Smiles)

8 0

4 years ago

Read 2 more answers

I know this might be a easy answer but with proper algebra format a chicken has two legs a dog has 4 legs the chicken must have

Rom4ik [11]

Step-by-step explanation:

Let each let of chicken be C and dog be D respectively.

Then as per question

2C+4D = 28.......i

and

C-D =14........ii

These are the two algebraic equation which you are looking for solve them

to get the answer

5 0

3 years ago