A chemist examines 15 sedimentary samples for nitrate concentration. The mean nitrate concentration for the sample data is 0.670 cc/cubic meter with a standard deviation of 0.0616.

a. Determine the 80% confidence interval for the population mean nitrate concentration. Assume the population is approximately normal. Round your answer to three decimal places.
b. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

(a) The 80% confidence interval for the population mean nitrate concentration is (0.648, 0.692).

(b) The critical value of t that should be used in constructing the 80% confidence interval is 1.345.

Step-by-step explanation:

Let X = nitrate concentration.

The sample mean nitrate concentration is, cc/cubic meter.

The sample standard deviation of the nitrate concentration is, .

It assumed that the population is approximately normal.

And since the population standard deviation is not known, we will use a t-interval.

The (1 - α)% confidence interval for population mean (μ) is:

(a)

The critical value of t for α = 0.20 and degrees of freedom, (n - 1) = 14 is:

*Use a t-table for the critical value.

Compute the 80% confidence interval for the population mean nitrate concentration as follows:

Thus, the 80% confidence interval for the population mean nitrate concentration is (0.648, 0.692).

(b)

The critical value of t for confidence level (1 - α)% and (n - 1) degrees of freedom is:

The value of  is:

α = 0.20

And the degrees of freedom is,

(n - 1) = 15 - 1 = 14

Compute the critical value of t for confidence level 80% and 14 degrees of freedom as follows:

*Use a t-table for the critical value.

Thus, the critical value of t that should be used in constructing the 80% confidence interval is 1.345.

3+x

step-by-step explanation:

here is me explaining it:

the pizza would be delivered around 5, give or take 15 minutes. this means it could be delivered anywhere from 4: 45 to 5: 15

let's say 5: 00 is equivalent to 0 on a number line and x represents time. 4: 45 would be equal to -15x because we are 15 minutes behind our starting point, 5: 00. 5: 15 would be equal to 15x because we are 15 minutes ahead of your starting point (which means you're late on the pizza delivery! )

absolute value is very confusing. the basic definition is how far you are from your starting point. if we deliver the pizza at 4: 45 (15 minutes before the starting point) we would be -15. this means we are 15 away from our starting point, 5: 00. that's the absolute value. |-15| (absolute value of negative fifteen) is equal to 15. if you did not understand this i suggest rereading this paragraph.

the normal way you would write this scenario would be 4.75 (4 and 3 quarters, or 4: 45. you can also write as a fraction.) is less than x and x is less than 5.25 (5 and 1 quarter or 5: 15). 4.75< x< 5.25 the reason why i am using numbers is because you cannot represent typical time as values on a graph, number line, or in an equation.

another way to write this scenario is with absolute value. we can write this as |x| being less than or equal to .25 (remember, this just means 15 minutes).           |x| ≤ .25.

sorry if the end was confusing. because we are talking about time this whole question is 10x harder. like i said earlier, you cannot represent time as, well, time, in a graph, equation, or number line. i set the values as follows: 1/4 or .25 for 15 minutes, and 1 for 1 hour. this is just a common way to set up graphs involving time.

|x| ≤ .25

i hope this ! : )

tell me if you need more assistance