You wish to test the following claim (Ha) at a significance level of a=0.001. For the context of this problem, Ha=H2-H1 where the first data set (µ1 ) represents the score on a Chemistry pre-test (taken before four weeks of tutoring) and the second data set (µ2) represents the score on a Chemistry post-test (taken after four weeks of tutoring). Ho: Hd = 0 Ha: Hd> 0 You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: Pre-Test Post-Test 47 51.6 40.4 22.9 42 52.4 42.7 34.1 37.4 38.3 40.1 34 45.2 30.5 43.6 44.5 40.1 53.8 40.5 58.4 44.4 32.9 43.9 46.3 42 37.9 44.7 31.8 48.2 47.2 38.4 46.7 43 51.8 49.1 61 43.1 66.9 44.8 51.8 49.7 64.1 46.1 59.2

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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.