Do piano lessons improve the spatial-temporal reasoning of preschool children? Neurobiological arguments suggest that this may be true. A study designed to test this hypothesis measured the spatial-temporal reasoning of 16 preschool children before and after six months of piano lessons. (The study also included children who took computer lessons and a control group; but we are not concerned with those here.) The changes in the reasoning scores are given below. 49 59047 0 4 4 -2 -2 5 1 2 6 (a) Find the mean, the standard deviation, and the standard error of the mean. S = SEM = (b) ive a 90% confidence interval for the mean improvement in reasoning scores. lower bound upper bound

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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.