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$5to10$

Short answer

One can be$90\%$confident that ${\mu }_1-{\mu }_2$lies somewhere between $10and5$

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

Step-by-step solution

Given Information

Given in the question that,

$90\%$CI from$5to10$ 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 $90$percent Cl is interpreted as a range of values containing the genuine population mean with probability $0.90or90\%$.

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$5to10$

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

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