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2 years ago

The ratio of boys to girls in a group is 4:1. If there are 33 more boys than girls, work out how many people there are in total.

Mathematics

2 answers:

MissTica2 years ago

7 0

Total number of people is 55

<u>Step-by-step explanation:</u>

Step 1:

Given ratio between boys and girls is 4:1. Let number of girls be x, so number of boys = 33 + x

⇒ 4x + x = x + 33 + x

⇒ 5x = 33 + 2x

⇒ 3x = 33

⇒ x = 11

Step 2:

Find total number of people.

33 + 2x = 33 + 22 = 55

WARRIOR [948]2 years ago

7 0

Answer:

There are 55 people altogether

Step-by-step explanation:

As the question says, there are 33 more boys than girls. So let's make girls = x as it is an unknown value:

boys = 33 + x

As we know that the ratio is 4:1 so, we can make it as:

4x : x

Given that the the ratio of boys is 4x and the value is 33+x. Now, we can compare it :

4x = 33 + x

4x - x = 33

3x = 33

x = 11

Next, we can add up all the people:

boys=>

4x = 4 × 11

= 44 boys

girls=>

x = 11 girls

altogether=>

44 + 11 = 55 people

(Correct me if I am wrong)

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A survey was conducted in the United Kingdom, where respondents were asked if they had a university degree. One question asked,

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Answer:

$z=\frac{0.121-0.0892}{\sqrt{0.101(1-0.101)(\frac{1}{373}+\frac{1}{639})}}=1.620$

$p_v =2*P(Z>1.620)=0.105$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the two proportions are not statistically different at 5% of significance

Step-by-step explanation:

Data given and notation

$X_{1}=45$ represent the number of correct answers for university degree holders

$X_{2}=57$ represent the number of correct answers for university non-degree holders

$n_{1}=373$ sample 1 selected

$n_{2}=639$ sample 2 selected

$p_{1}=\frac{45}{373}=0.121$ represent the proportion of correct answers for university degree holders

$p_{2}=\frac{57}{639}=0.0892$ represent the proportion of correct answers for university non-degree holders

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportions are different between the two groups, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{45+57}{373+639}=0.101$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.121-0.0892}{\sqrt{0.101(1-0.101)(\frac{1}{373}+\frac{1}{639})}}=1.620$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =2*P(Z>1.620)=0.105$

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