Question

The following measurements (in picocuries per liter) were recorded by a set of carbon monoxide detectors installed in a manufacturing facility: 346.6,343.2,305.5,354.1 Using these measurements, construct a 99% confidence interval for the mean level of carbon monoxide present in the facility. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

[273.917;400783]

Explanation:

Hello!

You have to estimate the mean level of carbon monoxide in the facility by making a 99% CI.

The variable is

X: carbon monoxide level measured by one detector.

X≈N(μ;σ²)

346.6, 343.2, 305.5, 354.1

n= 4

X[bar]= 337.35

S= 21.72

Since the variable is approximately normal and you don't know the value of the population variance, you have to use the t-statistic:

[X[bar] ±
`t_(n-1;1-\alpha /2)` *
`(S)/(√(n) )`]

`t_(n-1;1-\alpha /2)= t_(3;0.995)= 5.841`

[337.35 ± 5.841 *
`(21.72)/(√(4) )`]

[273.917;400783]

Using a 99% confidence level you'd expect that the population means of carbon monoxide in the facility.

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