Suppose That the Study in Problem #2 Was Performed with a Random

question 4

Essay

Suppose that the study in problem #2 was performed with a random sample of $n = 121$ patient contacts where a plain ring was worn, and 40 of these patient contacts resulted in bacterial transmission.
a) Describe the shape, center, and spread of the sampling distribution of $\hat { p }$ if the null hypothesis $H _ { o } : p = 0.25$ were true.






b) Is there convincing evidence that the null hypothesis is not true, or is $\hat { p }$ consistent with what you would expect to see if the null hypothesis were true? Carry out a hypothesis test to answer this question.

Calculate probabilities for simple and compound events.

Identify and apply the rules for calculating the complement of an event.

Understand probability models and their applications to real-world scenarios.

Comprehend and utilize the concepts of disjoint and non-disjoint events in probability contexts.

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Definitions:

Pinion

A small gear that engages with a larger gear or rack, often used to convert rotational motion to linear motion or vice versa.

Mechanical Advantage

The factor by which a mechanism multiplies the force put into it, enabling the lifting or moving of heavier loads with less effort.

Pitch Diameters

The effective diameter of a screw thread, halfway between the crests and roots, used in measuring and specifying thread sizes.

Diametral Pitches

Diametral pitches refer to the number of teeth per inch of the diameter of a gear, which determines the size of the teeth and the pitch of the gear.