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g The data below represent a random sample of 9 scores on a statistics quiz. (The maximum possible score on the quiz is 10.) Assume that the scores are normally distributed with a standard deviation of 2.3. Estimate the population mean with 95% confidence. 8,10,8,4,5,7,3,10,8 Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must

Answer :

Answer:

95% Confidence interval:  (5.5,8.5)

Step-by-step explanation:

We are given the following data in the question:

8,10,8,4,5,7,3,10,8

Sample size,n = 9

Population standard deviation = 2.3

Formula:

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{63}{9} = 7[/tex]

Sample mean = 7

95% Confidence interval:

[tex]\mu \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]

Putting the values, we get,

[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]

[tex]7 \pm 1.96(\dfrac{2.3}{\sqrt{9}} ) =7 \pm 1.5 = (5.5,8.5)[/tex]

is the required confidence interval for population mean.

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