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With 95% of confidence interval for the time it takes salesperson to talk to a potential customer is (12.42 , 5.38).
A Random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimizing the risk of selection bias.
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ ² ,s² ,Var(X) , or V(X).
A confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level represents the long-run proportion of corresponding CIs that contain the true value of the parameter. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.
Given in the question:
n = 46
x = 8.90
σ = 6
α = 0.95
As we know that:
[tex]X[/tex] ±[tex]Z_{\alpha /2} * \frac{\beta }{\sqrt{n} }[/tex]
putting the values we get,
8.90 ± Z (0.95/2) ×6/√46
Now, considering the positive sign, we get,
= 8.90 + 3.52
= 12.42
Now considering the negative sign,
8.90 ± Z (0.95/2) ×6/√46
= 8.90 - 3.52
= 5.38
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