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3 years ago

How can you tell if a set of bivariate data shows a linear relationship?

1 answer:

5 0

Make a scatterplot of the data. Once finished, look at the scatterplot to determine if the data taken holistically appears to be a close to the shape of a line.

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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

How much will it cost for him to buy 3 dozen using the rate $12.00 for 20 cookies?

Art [367]

3 dozen = 36 cookies

20/12 = 1.666666666666667

1.666666666666667 = 1 cookie

(x36)

36 x 1.666666666666667 = 60

It will cost him $60 for 3 dozen cookies

4 0

3 years ago

Four times a certain number decreased by twice the same number gives 17. the number is

Verdich [7]

Answer:

8.5

Step-by-step explanation:

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3 years ago

Angle C is inscribed in circle O AB is a diameter of O what is measure of A

TEA [102]

Answer:

A = 53 degree

90-37 = 53 degree

As the triangle is a right angle triangle we see complimentary to the other angles and as all angles in a triangle equal 180, we see the other two which compliment this.

Step-by-step explanation:

6 0

3 years ago

I'm doing math homework and the boy next to me asked what the mean to there numbers is, 22, 26, 28, 30, 39, 44, 62, and 63 what

AfilCa [17]

22+26+28+30+39+44+62+63= 314 Divide the answer by the amount of numbers =39.25

8 0

3 years ago

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