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GaryK [48]
3 years ago
13

ny with 350 employees is changing the employee health insurance plan to either plan A or plan B. The company wants to know if em

ployees have a preference between the two plans and whether or not preference differs between those employees who have family members covered under the current plan (group 1) and those who do not (group 2). The human resources office takes a simple random sample from each of the two groups, sends information about both plans to the employees in each sample, and asks them whether they prefer plan A or plan B. The table summarizes the responses received, with expected cell counts in parentheses. Plan A Plan B Total Yes (group 1) 40 (32.5) 20 (27.5) 60 No (group 2) 6 (13.5) 19 (11.5) 25 Total 46 39 85 Which statement is true about whether the conditions for the chi-square test for homogeneity have been met?
Mathematics
1 answer:
Marianna [84]3 years ago
7 0

Answer:

All the conditions for the chi square test of homogeneity are satisfied.

Step-by-step explanation:

The conditions for the chi square test  are

1) the sample is a random sample

2) the variable under study is categorical

3) all expected value of the number of sample observations are greater or equal to 5.

A)The observations must be independent

B) for 2 categories the expected values must be at least 5

C) for the 3 categories the expected values must be at least 1 and no more than 20% may be smaller than 5

The observations given are independent that is not equally likely i.e do not have equal chances of occurrences or are not dependent on each other.

4) the overall sample must be resonably large that is greater than 50

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5530 mm is 553 cm and 5.53 m.

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Expression 1 is -12x + 3
musickatia [10]

Answer:

-12 + 3 - (10x - 15x + 96)

Step-by-step explanation:

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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the
Orlov [11]

Answer:

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question:

p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015

What is the probability that the sample proportion will differ from the population proportion by less than 0.03?

This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So

X = 0.08

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.08 - 0.05}{0.015}

Z = 2

Z = 2 has a pvalue of 0.9772

X = 0.02

Z = \frac{X - \mu}{s}

Z = \frac{0.02 - 0.05}{0.015}

Z = -2

Z = -2 has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

6 0
3 years ago
Will give alot of points!
Rom4ik [11]
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What is the solution to this system of equations?<br>x-2y=15<br>2x + 4y=-18​
jeyben [28]

Answer:

x = 3; y = -6

Step-by-step explanation:

 x - 2y =  15

2x + 4y = -18​

Multiply both sides of the first equation by 2. Write the second equation below it, and add the two equations.

     2x - 4y = 30

(+)  2x + 4y = -18

---------------------------

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x - 2y = 15

3 - 2y = 15

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y = -6

Answer: x = 3; y = -6

4 0
3 years ago
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