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scoray [572]
3 years ago
6

Can anyone solve this​

Mathematics
1 answer:
MrMuchimi3 years ago
5 0
They are equal. It was explained above
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You are studying the water properties of a bog in eastern Wisconsin and wish to estimate its acidity. You de ne a grid that cove
GenaCL600 [577]

Answer:

4.8-1.453\frac{1.3}{\sqrt{82}}=4.591    

4.8+1.453\frac{1.3}{\sqrt{82}}=5.009    

So on this case the 85% confidence interval would be given by (4.591;5.009)    

And we can conclude that the true mean for the acidity at 85% of confidence is between  (4.591;5.009)    

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

df=n-1=82-1=81

Since the Confidence is 0.85 or 85%, the value of \alpha=0.15 and \alpha/2 =0.075, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.075,81)".And we see that t_{\alpha/2}=1.453

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

4.8-1.453\frac{1.3}{\sqrt{82}}=4.591    

4.8+1.453\frac{1.3}{\sqrt{82}}=5.009    

So on this case the 85% confidence interval would be given by (4.591;5.009)    

And we can conclude that the true mean for the acidity at 85% of confidence is between  (4.591;5.009)    

6 0
4 years ago
Read 2 more answers
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