Respuesta :
The confidence interval for the population mean with 99% confidence interval is (6.90;8.50).
What is meant by confidence interval?
A confidence interval is a set of values that, with a particular level of certainty, includes a population value. When a population mean is between an upper and lower interval, it is frequently stated as a percentage.
The population mean is mean [tex]\bar{x}[/tex]=7.3.
The sample's standard deviation is 2. 9
Number of samples: 42
The range of possibilities for the mean, [tex]\bar{x}[/tex]
The confidence interval for the mean is
[tex]\bar{x}[/tex] ± (σ/√n)
To calculate the critical value, we must first determine the degrees of freedom, which are given by:
df=n-1
df=42-1
df=41.
Since the confidence level is 0.99 or 99%, the values of and can be used to calculate the critical value using Excel, a calculator, or a table is 2.701
7.3-2.701(2.9/√42)=6.9013
7.3+2.701(2.9/√42)=8.5086
The 99% confidence interval in this instance would therefore be provided by (6.90;8.50).
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