The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location. Ceremonial Ranking Cooking Jar Sherds Decorated Jar Sherds (Noncooking) Row Total A 85 50 135 B 93 52 145 76 78 154 Column Total 254 180 434 A USE SALT Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance. (a) What is the level of significance? 0.05 State the null and alternate hypotheses. O Ho: Ceremonial ranking and pottery type are not independent. H, : Ceremonial ranking and pottery type are independent. Hoi Ceremonial ranking and pottery type are independent. H,: Ceremonial ranking and pottery type are not independent. O Ho: Ceremonial ranking and pottery type are not independent. H, : Ceremonial ranking and pottery type are not independent. O Họ: Ceremonial ranking and pottery type are independent. H,: Ceremonial ranking and pottery type are independent. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) ]x 5.991

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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.