Question

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 1

95% Confidence interval: (5.5,8.5)

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:

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(63)/(9) = 7`

Sample mean = 7

95% Confidence interval:

`\mu \pm z_(critical)(\sigma)/(√(n))`

Putting the values, we get,

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

`7 \pm 1.96((2.3)/(√(9)) ) =7 \pm 1.5 = (5.5,8.5)`

is the required confidence interval for population mean.