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2 years ago

Convert to scientific notation. 16,120

Mathematics

1 answer:

eduard2 years ago

6 0

Answer:

$1.612\times10^4$

Step-by-step explanation:

In order to find the notation of a number find the total number of 0's that the number has, and realize that all whole numbers have a invisible decimal point.

$1.612\times10^4$

Exponent is positive to move the decimal point to the right four times

$1.6.1.2.0.$

$= 16,120$

Hope this helps.

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Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".

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Solution to the problem

For this case we want to test:

H0: Absenteeism is distributed evenly throughout the week

H1: Absenteeism is NOT distributed evenly throughout the week

We have the following data:

Monday Tuesday Wednesday Thursday Friday Saturday Total

12 9 11 10 9 9 60

The level of significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{60}{6}= 10$ and the expected value is the same for all the days since that's what we want to test.

now we can calculate the statistic:

$\chi^2 = \frac{(12-10)^2}{10}+\frac{(9-10)^2}{10}+\frac{(11-10)^2}{10}+\frac{(10-10)^2}{10}+\frac{(9-10)^2}{10}+\frac{(9-10)^2}{10}=0.8$

Now we can calculate the degrees of freedom (We know that we have 6 categories since we have information for 6 different days) for the statistic given by:

$df=categor-1=6-1=5$

The critical value can be founded with the following Excel formula:

=CHISQ.INV(1-0.05,5)

And we got $\chi^2_{critc}= 11.0705$

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