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3 years ago

1. The equation c = 2.95g shows how much it costs to buy gas at a gas station on a

Mathematics

1 answer:

Karolina [17]3 years ago

7 0

Answer:

see the procedure

Step-by-step explanation:

we have

$c=2.95g$

where

c -----> the cost in dollars

g ----> the number gallons of gas purchased

1) For g=1 gal

substitute the value of g in the equation and solve for c

$c=2.95(1)$

$c=\$2.95$

The pair (1,2.95) fit the relationship

2) For g=3 gal

substitute the value of g in the equation and solve for c

$c=2.95(3)$

$c=\$8.85$

The pair (3,8.85) fit the relationship

3) For g=5 gal

substitute the value of g in the equation and solve for c

$c=2.95(5)$

$c=\$14.75$

The pair (5,14.75) fit the relationship

4) For c=$20.65

substitute the value of c in the equation and solve for g

$20.65=2.95g$

$g=20.65/2.95$

$g=7\ gal$

The pair (7,20.65) fit the relationship

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Dafna1 [17]

Answer:

a) $\bar d= \frac{\sum_{i=1}^n d_i}{n}=72.2$

$s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}} =9.311$

b) The 90% confidence interval would be given by (63.330;81.070)

$63.330 < \mu_{left}- \mu_{right}$

Step-by-step explanation:

1) Previous concepts and notation

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".

Let put some notation

x=left arm , y = right arm

x: 175 169 182 146 144

y: 102 101 94 79 79

The first step is define the difference $d_i=x_i-y_i$ , that is given so we have:

d: 73, 68, 88, 67, 65

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=72.2$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}} =9.311$

2) Confidence interval

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

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

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

$df=n-1=5-1=4$

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(0.05,4)".And we see that $t_{\alpha/2}=2.13$

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

$72.2-2.13\frac{9.311}{\sqrt{5}}=63.330$

$72.2+2.13\frac{9.311}{\sqrt{5}}=81.070$

So on this case the 90% confidence interval would be given by (63.330;81.070)

$63.330 < \mu_{left}- \mu_{right}$

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3 years ago