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Inessa [10]
3 years ago
8

If x is a rational number, then x + 12 could NOT be:

Mathematics
1 answer:
aalyn [17]3 years ago
5 0

Step-by-step explanation:

x  + 12 = 0

x =  - 12

hope it help you.

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3 years ago
The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15%
vagabundo [1.1K]

Answer:

1) \chi^2 =\frac{(112-150)^2}{150}+\frac{(95-75)^2}{75}+\frac{(210-200)^2}{200}+\frac{(83-75)^2}{75}=16.313

2) p_v =P(\chi^2_{3}>16.313)=0.000978

And we got the same decision reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts

The Chi-Square test of independence is used "to determine if there is a significant relationship between two nominal (categorical) variables". And is defined with the following statistic:

\chi^2 =\sum_{i=1}^n \frac{(O-E)^2}{E}

Where O rpresent the observed values and E the expected values.  

State the null and alternative hypothesis

Null hypothesis: The distribution  is 30% catfish, 15% bass, 40% bluegill, and 15% pike

Alternative hypothesis: The distribution  is NOT 30% catfish, 15% bass, 40% bluegill, and 15% pike

The observed values are given by the table given:

Catfish =112, BAss = 95, Bluegill=210, Pike=83

Calculate the expected values

In order to calculate the expected values we can use the following formula for each cell of the table

E = \% Grand total

E_{Catfish}=500*0.3=150

E_{Bass}=500*0.15=75

E_{Bluegill}=500*0.4=200

E_{Pike}=500*0.15=75

Part 1: Calculate the statistic

\chi^2 =\frac{(112-150)^2}{150}+\frac{(95-75)^2}{75}+\frac{(210-200)^2}{200}+\frac{(83-75)^2}{75}=16.313

\chi^2 =16.313

Calculate the critical value

First we need to calculate the degrees of freedom given by:

df= (categories-1)=(4-1)= 3

Since the confidence provided is 95% the significance would be \alpha=1-0.95=0.05 and we can find the critical value with the following excel code: "=CHISQ.INV(0.95,3)", and our critical value would be \chi^2_{crit}=7.815

We can calculate also the p value:

p_v =P(\chi^2_{3}>16.313)=0.000978

And we got the same decision reject the null hypothesis at 5% of significance.

5 0
3 years ago
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