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• Subject Name : Statistics

## Bumpus’s Data on Natural Selection

In an 1898 biology lecture at Woods Hole, Massachusetts, Hermon Bumpus reminded his audience that the process of natural selection for evolutionary change was an unproved theory: ”Even if the theory of natural selection were as firmly established as Newton’s theory of attraction of gravity, scientific method would still required frequent examination of its claims.” As evidence in support of natural selection, he presented measurements on house sparrows brought to the Anatomical Laboratory of Brown University after an uncommonly severe winter storm. Some of these birds had survived and some had perished. Bumpus asked whether those that perished did so because they lacked physical characteristics enabling them to withstand the intensity of that particular instance of selective elimination.

Is humerus length related to whether the bird would survive or perish? That’s the question being addressed by Case Study 2.1 in the Sleuth.

A total of 59 subjects are included in the data: 35 are adult male sparrows that survived and 24 that perished.

Humerus Status

Min. :659.0 Perished:24

1st Qu.:724.5 Survived:35

Median :736.0

Mean :733.9

3rd Qu.:747.0

Max. :780.0

Status min Q1 median Q3 max mean sd n missing1 Perished 659 718.25 733.5 743.25 765 727.9167 23.54259 24 02 Survived 687 728.00 736.0 751.50 780 738.0000 19.83906 35 0

Both distributions are approximately normally distributed.

data: Humerus by Statust = -1.777, df = 57, p-value = 0.0809alternative hypothesis: true difference in means is not equal to 095 percent confidence interval: -21.446053 1.279386sample estimates:mean in group Perished mean in group Survived 727.9167 738.0000

## The Space Shuttle Challenger Explosion and the O-ring

Below is the key graph of the O-ring test data that NASA analyzed before launch. Take a look and see if you can spot any pattern between temperature on the day of the test and O-ring failure rate.

Of the many launches at high temperature (>65°F) in the second graph, a smaller percentage had O-ring problems (15%). In the very few launches at low temperatures, 100% had O-ring problems (and these were only tested between 50°F and 65°F, not the even colder 31°F at launch).

## The Big Bang Theory

EdwinHubbleusedthepoweroftheMountWilsonObservatorytelescopestomeasurefeaturesofnebulae outside the Milky Way. He was surprised to find a relationship between a nebula’s distance from earth and the velocity with which it was going away from the earth. Hubble’s initial data on 24 nebulae are shown as a scatterplot in Figure 1. (Data from Hubble, ”A Relation Between Distance and Radial Velocity Among Extra-galactic Nebular,” Proceedings of the National Academy of Science 15 (1929): 168-73.) The horizontal axis measures the recession velocity, in kilometers per second, which was determined with considerable accuracy by the red shift in the spectrum of light from a nebula. The vertical scale measures distance from the earth, in megaparsecs: 1 megaparsec is 1 million parsecs, and 1 parsec is about 30.9 trillion kilometers. Distances were measured by comparing mean luminosities of the nebulae to those of certain star types, a method that is not particularly accurate.

The summary of the data that was given in big bang when performed exploratory analysis we found the following values

summary(Distance Yi`) Min. 1st Qu. Median Mean 3rd Qu. Max. 0.0320 0.4062 0.9000 0.9114 1.1750 2.0000 summary(Velocity Xi`) Min. 1st Qu. Median Mean 3rd Qu. Max. -220.0 165.0 295.0 373.1 537.5 1090.0

When performing linear regression to plot the line between velocity and distance we got the following values

lm(formula = `Distance Yi` ~ `Velocity Xi`) Coefficients: (Intercept) `Velocity Xi` 0.399098 0.001373

The intercept value is not zero and the line plotted is a straight line between velocity and distance. The distance (Y ) between them and the velocity (X ) at which they appear to be going away from each other satisfy the relationship (Y /2) / VT = (X /2) / V = sin(A),Where A is half the angle between them. In that case, Y = 0.399098 is a straight line relationship between distance and velocity. The points in Figure 1. do not fall exactly on a straight line. It might be, however, that the mean of the distance measurements is TX. The slope parameter T in the equation Mean{Y} = 0.001373 is the time elapsed since the Big Bang.

Remember, at the center of any academic work, lies clarity and evidence. Should you need further assistance, do look up to our Statistics Assignment Help

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