The value of 4.63 falls within the interval (4.66, 4.791) where 95% of the sample means occur option (B) is correct.
What is a confidence interval for population standard deviation?
It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
The formula for finding the confidence interval for population standard deviation as follows:
[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]
Where s is the standard deviation.
n is the sample size.
[tex]\chi^2_{\alpha/2, \ n-1} and \chi^2_{1-\alpha/2, \ n-1}[/tex] are the constant based on the Chi-Square distribution table.
α is the significance level.
σ is the confidence interval for population standard deviation.
Calculating the confidence interval for population standard deviation:
We know significance level = 1 - confidence level
It is given that:
Mean of the population x = 4.73
Standard deviation s = 0.865
Sample size n = 200
The interval where 95% of the sample means occur:
Lower limit = 4.73 - 0.865/√200
Lower limit = 4.66
Upper limit = 4.73 + 0.865/√200
Upper limit = 4.791
The interval = (4.66, 4.791)
Thus, the value of 4.63 falls within the interval (4.66, 4.791) where 95% of the sample means occur option (B) is correct.
Learn more about the confidence interval here:
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