What is the proportional relationship with the table?

An automobile club reported that the average price of regular gasoline in a certain state was $2.61 per gallon. The following d

laila [671]

Answer:

$2.618-2.98\frac{0.078}{\sqrt{15}}=2.56$

$2.618+2.98\frac{0.078}{\sqrt{15}}=2.68$

So on this case the 99% confidence interval would be given by (2.56;2.68)

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:

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

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=2.618$

The sample deviation calculated $s=0.078$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=15-1=14$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that $t_{\alpha/2}=2.98$

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

$2.618-2.98\frac{0.078}{\sqrt{15}}=2.56$

$2.618+2.98\frac{0.078}{\sqrt{15}}=2.68$

So on this case the 99% confidence interval would be given by (2.56;2.68)

5 0

3 years ago

If the measure of angle one is 160° then the measure of angle five=

trapecia [35]

Based on limited information, it can only be inferred that angle give is either 160 degrees or 20 degrees.

4 0

3 years ago

Lea has 3/4 cup of laundry detergent left in detergent bottle. Each load of laundry requires 1/6 cup of detergent. How many load

Stells [14]

ANSWER

Lea can wash 4½ loads of laundry with the remaining detergent.

EXPLANATION

Quantity of detergent left
$= \frac{3}{4}$

Quantity required to watch each load
$= \frac{1}{6}$

Number of loads Lea can wash
$= \frac{3}{4} \div \frac{1}{6}$

We now simplify this by multiplying with the reciprocal

Number of loads Lea can wash

$= \frac{3}{4} \times \frac{6}{1}$

$= \frac{3}{2} \times \frac{3}{1}$

$= \frac{9}{2}$

$= 4 \frac{1}{2}$

Therefore Lea can wash 4½ loads of laundry with the remaining detergent.

3 0

3 years ago

Please help me! I’ll name you brainiest!!!

Kamila [148]

Answer:

80

Step-by-step explanation:

first, put in (5x-4) for the x in g(x).

g(f(x))=(5x-4)^2 -1

now, FOIL and simplify.

25x^2-40x+16-1

25x^2-40x+15

now, plug in -1 for x.

25(-1)^2-40(-1)+15

25+40+15

80

8 0

3 years ago

Read 2 more answers

Dustin has three lengths of rope: 3/4 yard long, 2/3 yard long, and 7/10 yard long. He needs at least 1 yard of rope. Which two

ad-work [718]

A think it is all of the above because each rope is the same amount

6 0

3 years ago

Read 2 more answers