Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
The 99% confidence interval for the true mean IQ score for all children of this group is (97.4, 102.6). The lower limit is 97.4 and the upper limit is 102.6.
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 - 0.99}{2} = 0.005[/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 - 0.005 = 0.995[/tex], so Z = 2.575.
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 = 2.575\frac{10}{\sqrt{100}} = 2.575[/tex]
Rounding to one decimal place, the margin of error is 2.6.
The lower end of the interval is the sample mean subtracted by M. So it is 100 - 2.6 = 97.4.
The upper end of the interval is the sample mean added to M. So it is 100 + 2.6 = 102.6.
The 99% confidence interval for the true mean IQ score for all children of this group is (97.4, 102.6). The lower limit is 97.4 and the upper limit is 102.6.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
