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FromTheMoon [43]
3 years ago
5

You have drawn a simple random sample of 36 college students, asking each student how much rent they pay per month. You obtain a

sample mean of 573 and a sample standard deviation of 22. Calculate the upper confidence limit of a 90% confidence interval for the population mean of rent paid. If necessary, round your answer to four decimal places. HINT: For a confidence interval of [a,b] we refer to "a" as the "lower confidence limit" and we refer to "b" as the "upper confidence limit". g
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
6 0

Answer:

573-1.690\frac{22}{\sqrt{36}}=566.8033    

573+1.690\frac{22}{\sqrt{36}}=579.1967      

And the 90% confidence interval would be between [566.80 and 579.20]

Step-by-step explanation:

Information given

\bar X=573 represent the sample mean

\mu population mean (variable of interest)

s=22 represent the sample standard deviation

n=36 represent the sample size  

Confidence interval

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The degrees of freedom are given by:

df=n-1=36-1=35

The Confidence level is 0.90 or 90%, the significance would be \alpha=0.1 and \alpha/2 =0.05, and the critical value for this case would be t_{\alpha/2}=1.690

And replacing we got:

573-1.690\frac{22}{\sqrt{36}}=566.8033    

573+1.690\frac{22}{\sqrt{36}}=579.1967    

And the 90% confidence interval would be between [566.8033 and 579.1967]

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