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.

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d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;