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3 years ago

Eli,Freda and geoff where given £800 to share in the ratio of there ages

Mathematics

2 answers:

Ilia_Sergeevich [38]3 years ago

8 0

Answer 180, 260 and 360

Step-by-step explanation

Eli age = 9

Freda age = 13

Geoff age = 18

We write the ages in ratio as 9 : 13 : 18

Now sum all the ages 9 + 13 + 18 = 40

The total amount to be shared is £800

Therefore Eli share = 9/40 x £800 = £180

Freda share = 13/40 x £800 = £260

Geoff share = 18/40 x £800 = £360

Valentin [98]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The ratio received = 9 : 13 : 18

Sum the parts of the ratio 9 + 13 + 18 = 40

Divide the amount by 40 to find the value of one part of the ratio

$\frac{800}{40}$ = £20 ← value of 1 part of ratio

Eli gets 9 × £20 = £180

Freda gets 13 × £20 = £260

Geoff gets 18 × £20 = £360

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The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15%

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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 $\chi^2_{crit}=7.815$