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hoa [83]
3 years ago
5

Solve each equation for the variable

Mathematics
1 answer:
motikmotik3 years ago
6 0

Answer:

X= -50

Step-by-step explanation:

Remove the parenthesis

multiply both sides by two

x - 6 =  -56

Move the 6 to the other side

x = -56 + 6

x = -50

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Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central district. The city plans to pay
andrezito [222]

Answer:

a) For this case we need to use a t distribution since we know the information about a sample and we don't know the population deviation.

b) 126-1.77\frac{15}{\sqrt{14}}=118.904    

126+1.77\frac{15}{\sqrt{14}}=133.096    

So on this case the 90% confidence interval would be given by (118.904;133.096)

c) For this case since confidence interval include tha value of 130 so then we don't have enough evidence to conclude that the claim by the consultant is incorrect.    

Step-by-step explanation:

Part a

For this case we need to use a t distribution since we know the information about a sample and we don't know the population deviation.

Part b

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.

\bar X=126 represent the sample mean

\mu population mean (variable of interest)

s=15 represent the sample standard deviation

n=14 represent the sample size  

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

df=n-1=14-1=13

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(0.05,13)".And we see that t_{\alpha/2}=1.77

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

126-1.77\frac{15}{\sqrt{14}}=118.904    

126+1.77\frac{15}{\sqrt{14}}=133.096    

So on this case the 90% confidence interval would be given by (118.904;133.096)

Part c

For this case since confidence interval include tha value of 130 so then we don't have enough evidence to conclude that the claim by the consultant is incorrect.    

6 0
3 years ago
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