Respuesta :
The confidence interval indicates that we are 95% sure that the mean height is within 0.4 inches of the sample mean of 6 feet and 5 inches.
For a smaller sample size, the confidence interval would become larger.
With a higher level of confidence, the confidence interval would become larger.
What is a z-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
- [tex]\overline{x}[/tex] is the sample mean.
- z is the critical value.
- n is the sample size.
- [tex]\sigma[/tex] is the standard deviation for the population.
The interpretation of an interval is that we are x% sure that the population mean is in that interval, in which x% is the confidence interval. Hence, considering the margin of error and the sample mean for this problem, the confidence interval indicates that we are 95% sure that the mean height is within 0.4 inches of the sample mean of 6 feet and 5 inches.
The margin of error equation means that:
- A decrease in n leads to a higher margin of error, hence a larger confidence interval.
- An increase in the confidence level leads to a higher value of z, so there is a higher margin of error, hence a larger confidence interval.
More can be learned about confidence intervals at https://brainly.com/question/25890103
#SPJ1
