Problem 2: The Centers for Disease Control and Prevention reported a survey of randomly selected Americans age 65 and older, which found that 535 of 106 women and 411 of 1012 men suffered from some form of arthritis. a) Find the sample proportion of arthritis for both genders. b) Do we have some evidence to suggest that there is one gender that suffers some form of arthritis more than the other gender? Explain your answer.

Problem 2: The Centers for Disease Control and Prevention reported a survey of randomly selected Americans age 65 and older, which found that 535 of 106 women and 411 of 1012 men suffered from some form of arthritis. a) Find the sample proportion of arthritis for both genders. b) Do we have some evidence to suggest that there is one gender that suffers some form of arthritis more than the other gender? Explain your answer.

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Description: Can I get some help on problem 2 A-C Problem 2: The Centers for Disease Control and Prevention reported a survey of randomlyselected Americans age 65 and older, which found that 535 of 106 women and 411 of 1012 mensuffered from some form of arthritis

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.

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Question

Can I get some help on problem 2 A-C

Problem 2: The Centers for Disease Control and Prevention reported a survey of randomly
selected Americans age 65 and older, which found that 535 of 106 women and 411 of 1012 men
suffered from some form of arthritis.
a) Find the sample proportion of arthritis for both genders.
b) Do we have some evidence to suggest that there is one gender that suffers some form of
arthritis more than the other gender? Explain your answer.
c) Construct a 95% confidence interval for the true difference in proportions of arthritis between
these two genders. Use Confidence Interval for the Difference in Proportions Calculator -
Statology to do the calculations.

Expert Solution

Part a)

For sample 1 (Women), we have that the sample size is $N_{1} = 1062$ , the number of favorable cases are $X_{1} = 535$ , so then the sample proportion is $\hat p_1 = \frac{X_1}{N_1} = \frac{ 535}{ 1062} = 0.5038$ ${\hat{p}}_{1} = \frac{535}{1062} \approx 0.5038$ .

For sample 2 (Men), we have that the sample size is $N_{2} = 1012$ , the number of favorable cases are $X_{2} = 411$ , so then the sample proportion is $\hat p_1 = \frac{X_1}{N_1} = \frac{ 535}{ 1062} = 0.5038$ ${\hat{p}}_{2} = \frac{411}{1012} \approx 0.4061$ .

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