Question

In each of exercise 10.13-10.18, we have presented a confidence interval for the difference,${\mu }_{1}and{\mu }_2$, between two population means. interpret each confidence interval.

$95\%$CI is from$-20to-15$

Short answer

One can be$95\%$confident that ${\mu }_1-{\mu }_2$lies somewhere between $-20$and $-15$

Equivalently one can be $95\%$confident that ${\mu }_1$is somewhere$15and20$less than${\mu }_2$.

Step-by-step solution

Given Information

Given in the question that,

$95\%$CI is from$-20to-15$ we have to interpret it.

Explanation

The mean found in a sample is thought to represent the best estimate of the population's true value. The sample mean of $95\%$Cl is read as a range of values including the genuine population mean with a probability of $0.95or95\%$.

Finding a confidence interval for the difference between two means can be used to compare two population means.

Assume that${\mu }_1$is the mean of a variable in population $1$and ${\mu }_2$is the mean of a variable in population $2$. The sampling distribution of the difference between two means is then ${\mu }_1-{\mu }_2$

Given a $95$percent confidence interval, Cl ranges from$-20to-15$

The confidence interval's endpoints are both negative values in this case.

This means that ${\mu }_1-{\mu }_2$is $95\%$certain to exist someplace.

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