Question

In each of exercise 10.13-10.18, we have presented a confidence interval for the difference,${\mu }_1-{\mu }_2$, between two population means. interpret each confidence interval

$90\%$CI from$-10to-5$

Short answer

One can be$90\%$confident that ${\mu }_1-{\mu }_2$lies somewhere between $-10and-5$

Equivalently one can be $90\%$confident that ${\mu }_1$is somewhere$5and10$less than${\mu }_2$.

Step-by-step solution

Given Information

Given in the question that,

$90\%$CI from$-10to-5$. we have to calculate the interpretation of confidence level.

Explanation

The mean found in a sample is thought to represent the best estimate of the population's true value. The sample mean of $90\%$Cl is read as a range of values including the genuine population mean with a probability of $0.90or90\%$.

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 $90\%$percent confidence interval, Cl ranges from$-10to-5$

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

This means that ${\mu }_1-{\mu }_2$is $90\%$certain to exist someplace.