Question

The planetary boundary layer (PBL) is the lowest layer of the troposphere; its characteristics are influenced by contact with the ground. Wind speed, temperature, and moisture in the PBL all affect weather patterns around the globe. A random sample of days was obtained and the height of the PBL (in meters) above the Great Basin Desert was measured using weather radar. Assume the underlying distribution of PBL heights is normal.
Height(m)
1 673 2 664 3 906 4 956 5 751 6 752 7 654
8 610 9 816 10 667 11 690 12 657 13 920 14 741 15 646 16 682 17 715
18 618 a. Find a 95% confidence interval for the true mean height of the PBL above the Great Basin Desert. b. Is there any evidence to suggest that the true mean height of the PBL above the Great Basin Desert is different from 700 m? There is_____to suggest that the mean height is different from 700 m. The confidence interval_____the value 700 so it is_____as the true mean height of the PBL.

Answer 1

The confidence interval for the true mean height of the PBL above the Great Basin Desert is (651.48,748.52) and there is any sufficient evidence that the true mean is different from 700 m .

Given Heights in meters: 673,664,906,956,751,752,654,610,816,667,690,657,920,741,646,682,715,618 and confidence level of 95%.

We have to show the evidence that the true mean height is different from 700 m.

We have to first make hypothesis.

$H_{0}:$μ=700

$H_{1}$:μ≠700

We have to first find the population standard deviation.

σ=$\sqrt{(x-x bar)^{2}/n-1 }$

=$\sqrt{187375.1/17}$

=104.98

Z=(X-μ)/σ

=(700-728.78)/104.98      (μ=728.78 is calculated in figure)

=-0.2741

p value of -0.2741 =0.39358

0.39358

0.39358<0.90

so we reject the null hypothesis.

Which means that the true mean is different from 700m.

Confidence level=X±z*s/$\sqrt{n}$

Upper level=700 +1.96*104.98/$\sqrt{18}$

=700+48.52

=748.52.

Lower level=700-1.96*104.98$\sqrt{18}$

=700-48.52

=651.48

Hence the confidence interval is (651.48,748.52).

Learn more about confidence interval at brainly.com/question/15712887

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