Respuesta :
Answer:
The 98% confidence interval estimate of the mean is between 32.45 hg and 34.75 hg.
32.3 is not a part of the confidence interval, which means that yes, these results are very different from the confidence interval 32.3 hg
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{6.2}{\sqrt{157}} = 1.15[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 33.6 - 1.15 = 32.45 hg
The upper end of the interval is the sample mean added to M. So it is 33.6 + 1.15 = 34.75 hg
The 98% confidence interval estimate of the mean is between 32.45 hg and 34.75 hg.
Are these results very different from the confidence interval 32.3 hg
32.3 is not a part of the confidence interval, which means that yes, these results are very different from the confidence interval 32.3 hg
