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Diano4ka-milaya [45]
3 years ago
8

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

ata show the price per gallon of regular gasoline for 15 randomly selected stations in the state. Complete parts a through c below. 2.69 2.51 2.54 2.72 2.55 2.57 2.59 2.73 2.67 2.72 2.66 2.59 2.66 2.52 2.55 a. Construct a 99​% confidence interval to estimate the average price per gallon of gasoline in the state. The 99​% confidence interval to estimate the average price per gallon of gasoline in the state is from ​$ nothing to ​$ nothing. ​(Round to the nearest​ cent.)
Mathematics
1 answer:
laila [671]3 years ago
5 0

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)    

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Read 2 more answers
A baseball team plays in a stadium that holds 50000 spectators. When the ticket price is $10, the average attendance is 27000. W
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Answer:

the answer is below

Step-by-step explanation:

Demand seems to be based on price.

Therefore we must consider two things:

that "x" is equal to the price and that "y" is equal to the average attendance.

Thus:

the two points would be:

(x1, y1) = (10,27000)

(x2, y2) = (6.39000)

The slope of a straight line is given by:

m = (y2-y1) / (x2-x1)

we replace:

m = (39000 - 27000) / (6 - 10) = 12000 / -4 = -3000

The equation of a straight line can be expressed like this

y = m * x + b.

where

m is the slope and b is the y-intercept.

we replace

y = -3000 * x + b.

To solve for b, replace x and y with the value of one of the points on the line.

We choose (6.39000). and we replace:

39000 = -3000 * 6 + b

39000 = -18000 + b

39000 + 18000 = b

b = 57000.

if we replace we have:

the equation becomes y = -3000 * x + 57000

since it is the demand and * x is the price.

t = d (x), therefore the equation becomes

d (x) = -3000 * x + 57000.

d (x) = 57000 - 3000 * x.

when x = 0, the price is 0 and the demand will be 57000, which will be more than the stadium can contain because the stadium can only contain 50,000.

So:

when x = 6, the price is 6 and the demand is 57000 - 18000 = 39000.

when x = 10, the price is 10 and the demand is 57000 - 30000 = 27000.

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3 years ago
2. The population in the South in 2000 was 100,236,820. In 2010, the population in the South had increased by 14.3% from 2000. A
vovangra [49]
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