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Featured 10 months ago

Draw a **Venn Diagram** (see below)

If you sum the dog and cat owners ...

**intersection** of the two categories (see Venn diagram below) was **counted twice** . The value of the intersection (both cat and dog owners) is

**own both a cat and a dog** .

The count of **owners of a dog and no cat** is

hope that helped

Featured 10 months ago

Choose the closest value in the table.

When the degrees of freedom is very high, the value of the inverse function changes very slowly. This is the case for Student's t-distributions and Chi-Squared where we are normally using the table to look up a value which corresponds to some cumulative probability being met.

These tests are most sensitive when the number of degrees of freedom is low - that's where all the action is. What they are telling us is that if we gather more data (more degrees of freedom) then our answer will get better. But there is a diminishing return as we gather more data, to the point that another point really doesn't change the test by a significant amount. This is reflected in our tables, where at some point they start skipping values and taking larger steps. This can be seen in the following graph, showing a student's t test for an

As the degrees of freedom gets very large the change becomes insignificant, so most tables jump from some high number, like 30, to

So the rule of thumb is to choose the table row closest to the degrees of freedom that you have. The error in doing so will be small, but you can, if you like, interpolate between the values.

If your degrees of freedom is larger than the largest integer entry in the table, use the value for

Featured 10 months ago

There is no single simple answer. It depends on additional parameters that are not given.

See explanation below.

Important parameters that are not given in this problem are distribution of goods among stores and the number of customers buying in these stores.

Let's try to address a problem generally, and then we will make certain reasonable assumptions.

The distribution of goods among stores is related to probability of customers to buy goods in each specific store.

Assume that the probability of a single item to be bought at store

Assume further that the total number of items purchased is

Consider now a store

This is a Bernoulli random variable.

Its mathematical expectation is

its variance is

its standard deviation is

The wholesaler has certain number

For instance, if we are talking about bottles of soda, it must be thousands per store.

Consider now

Here random variable

Obviously, the sum of the above random variable is a random variable equal to the number of items bought at

Let's analyse the distribution of probabilities of

First of all, according to the Central Limit Theorem, this distribution should be very close to Normal.

Since it's a sum of independent identically distributed random variables, its expectation is a sum of expectations of its components and its variance is a sum of variances:

It's time to make some additional assumption. To simplify the problem, let's assume that all stores are approximately equal in the number of customers who buy there. Therefore, the probability of a single item to be bought in store

That makes all

Let's say, we want to determine the probability of purchases in store

In this case

According to the "rule of 2

So, under the condition of equal probabilities of purchase in different stores

The second part of this problem is related to probability of **ANY** store purchase not to exceed 50% of its average. With certain degree of precision it can be calculated as the **product of corresponding probabilities** in **EACH** store.

To achieve 95% certainty that number of purchases in any store would not exceed 95%, we need the probability of each store to be

To achieve this probability for each store we need the number of purchases to be very high. "Rule of 3

Thus, with

which is about 43% of the average, so it's sufficient to have 100,000 items to distribute to make sure that none of the store would have more than 50% extra purchases with certainty of 95%.

If, evenly distributing 100,000 items among 500 relatively equivalent (in average number of purchases) stores, **at least one** store exceeded its sale by more than 50%, something abnormal and unexpected happened.

Please refer to Unizor for details on probabilities and statistics.

Featured 7 months ago

Since the events are independent,

Featured 3 months ago

An F-test assumes that data are normally distributed and that samples are independent from one another.

An F-test assumes that data are normally distributed and that samples are independent from one another.

Data that differs from the normal distribution could be due to a few reasons. The data could be skewed or the sample size could be too small to reach a normal distribution. Regardless the reason, F-tests assume a normal distribution and will result in inaccurate results if the data differs significantly from this distribution.

F-tests also assume that data points are independent from one another. For example, you are studying a population of giraffes and you want to know how body size and sex are related. You find that females are larger than males, but you didn't take into consideration that substantially more of the adults in the population are female than male. Thus, in your dataset, sex is not independent from age.

Featured 4 weeks ago

To find this, we need to know the number of ways the jury can be picked overall, and then the number of ways 6 men and 6 women can be on the jury. The fraction of the two will be the probability.

The total number of ways the jury can be picked is the combination of a pool of 30 people and choosing 12:

and now let's evaluate this:

Ok - we know the number of ways the jury can be picked. Now how many ways can the jury consist of 6 men and 6 women?

For the men, there are 15 in the pool and we're picking 6:

and now let's evaluate that:

The same number of choices of women are available, so we multiply the number of men's choices and women's choices:

And now we can find the probability:

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