Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
a) The 95% confidence interval for the lead concentration in water from this source is between 11.23 µg/L and 13.77 µg/L.
b) The upper bound of the confidence interval is less than 14 µg/L, which means that yes, we can conclude that the lead concentration is less than 14µg/L.
Step-by-step explanation:
We have the standard deviation for the samples, which mean that the t-distribution will be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 12 - 1 = 11
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.201
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.201\frac{2}{\sqrt{12}} = 1.27[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 12.5 - 1.27 = 11.23 µg/L.
The upper end of the interval is the sample mean added to M. So it is 12.5 + 1.27 = 13.77 µg/L.
The 95% confidence interval for the lead concentration in water from this source is between 11.23 µg/L and 13.77 µg/L.
(b) Can you conclude that the lead concentration is less than 14µg/L?
The upper bound of the confidence interval is less than 14 µg/L, which means that yes, we can conclude that the lead concentration is less than 14µg/L.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
