Noise levels at 6 airports were measured in decibels yielding the following data: 144,119,140,143,128,112 Construct the 99% confidence interval for the mean noise level at such locations. Assume the population is approximately normal. Step 1 of 4 : Calculate the sample mean for the given sample data. Round your answer to one decimal place.

99% Confidence interval for the population mean noise level = (110.8, 151.2) in decibels

Step-by-step explanation:

Noise levels = 144,119,140,143,128,112

Sample mean = xbar = (sum of all data)/(sample size)

Sample mean = (Σx)/N = (144 + 119 + 140 + 143 + 128 + 112)/6 = 131.0 to 1 d.p

Standard deviation = √[Σ(x - xbar)²/N]

Σ(x - xbar)² = [144 - 131]² + [119 - 131]² + [140 - 131]² + [143 - 131]² + [128 - 131]² + [112 - 131]²

= 169 + 144 + 81 + 144 + 9 + 361 = 908

Standard deviation = √(908/6) = 12.30.

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 131 dB

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 6 - 1 = 5.

Significance level for 99% confidence interval

(100% - 99%)/2 = 0.5% = 0.005

t (0.005, 5) = 4.032 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 12.30

n = sample size = 6

σₓ = (12.30/√6) = 5.02

99% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 131 ± (4.032 × 5.02)

CI = 131 ± 20.24064

99% CI = (110.75936, 151.24064)

99% Confidence interval = (110.759, 151.241)

Hope this Helps!!!