Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Answer:
n = 133.
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 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
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.
Standard deviation of the times is 14 hours.
This means that [tex]\sigma = 14[/tex]
How large a sample should be taken to get the desired interval?
Within 2 hours, which means that we want n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.645\frac{14}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.645*14[/tex]
Dividing both sides by 2
[tex]\sqrt{n} = 1.645*7[/tex]
[tex](\sqrt{n})^2 = (1.645*7)^2[/tex]
[tex]n = 132.6[/tex]
Rounding up, n = 133.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
