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 include the parentheses and the comma between the confidence limits. Confidence Interval

So on this case the 95% confidence interval would be given by (5.497;8.503)    

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".

represent the sample mean for the sample  

population mean (variable of interest)

represent the population standard deviation

n represent the sample size  

Solution to the problem

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

  (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

(2)  

(3)  

The mean calculated for this case is

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that

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

So on this case the 95% confidence interval would be given by (5.497;8.503)    

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step-by-step explanation: