This is a test i'm taking there's 8 questions. This is due today it would be great if I got help on all the questions

A classic rock radio station claims to play an average of 50 minutes of music every hour. However, it seems that every time you

tia_tia [17]

Answer:

a) $47.917-1.796\frac{2.811}{\sqrt{12}}=46.460$

$47.917+1.796\frac{2.811}{\sqrt{12}}=49.374$

b) Null hypothesis: $\mu =50$

Alternative hypothesis: $\mu \neq 50$

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

We have the following data: 44 49 45 51 49 53 49 44 47 50 46 48

And we can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s= \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

And replacing we got:

$\bar X= 47.917, s= 2.811$

$\mu$ population mean (variable of interest)

n=12 represent the sample size

Part a: Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are given:

$df= n-1= 12-1=11$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,11)".And we see that $t_{\alpha/2}=1.796$

Now we have everything in order to replace into formula (1):

$47.917-1.796\frac{2.811}{\sqrt{12}}=46.460$

$47.917+1.796\frac{2.811}{\sqrt{12}}=49.374$

Part b

For this case the system of hypothesis are:

Null hypothesis: $\mu =50$

Alternative hypothesis: $\mu \neq 50$

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

6 0

3 years ago

How do the expressions 4(3+x) and (3+3+3+3) + (x+x+x+x) compare to one another

Dafna1 [17]

Answer:

Step-by-step explanation:

If we expand 4(3+x), we get (4*3)+(4*x).

Then we do 4*3 to get 12 and 4*x to get 4x

(3+3+3+3) is the same thing as 4*3, because we are adding 3 together 4 times. (3+3+3+3) gives us 12 as well, since they are the same thing.

(x+x+x+x) is the same thing because we are adding x together 4 times, which is the same thing as (4*x). (x+x+x+x) gives us 4x as well.

Hope this helps.

3 0

3 years ago

Read 2 more answers

The degree of the polynomial function f(x) is 3.

yawa3891 [41]

Answer:

3rd graph.

Step-by-step explanation:

Roots of the equation are where the graph crosses the x axis. So the bottom left (3rd) graph is correct.

3 0

3 years ago

A piece of plywood was cut so it's length with 8 ft by 4 ft what is the area of the wood

Elena L [17]

The area of an object is found by multiplying the length by the width, so to solve your problem, multiply 8*4 to get 32.

8 0

4 years ago

A farmer Has 900 yards of fencing to enclose a rectangular pasture for her goats. Since one side of the pasture borders a river,

horsena [70]

Answer:

Length, l=450 yards

Width, b=225 yards

Step-by-step explanation:

Let the long side be x and since the length is twice the width, then the width is half of that length hence 0.5x. Since we only have three parts to fence as one long side doesn't require fencing, then the perimeter will be given by x+0.5x+0.5x=2x=900 yards

X=900/2=450 yards for long side.

The short side is 0.5x hence 0.5*450=225 yards

In conclusion, the long side is 450 yards while short side is 225 yards.

7 0

3 years ago