Bill Alther is a zoologist who studies Anna's hummingbird (Calypteanna). A random sample of nine of these birds was caught, weighed, and released in a remote part of the Grand Canyon. The weights observed (in grams) were : 3.7 2.9 3.8 4.2 4.8 3.1 3.5 4.3 3.0 Let x be a random variable representing weights of Anna's hummingbirds in this part of the Grand Canyon. Assuming x has a normal distribution with sample standard deviation 0.648. The population mean is 4.55 grams. (a) Calculate the Sample Mean of the above mentioned data values. (b) Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less tham 4.55 grams? Establish the Null and AIternate Hypothesis. (c) Compute the Test statistics of the sample data using Student's t-distribution table. Take a= 0.05 (d) Find the P-value or range of P-values. (e) Conclude the test and interpret the result.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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