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vlabodo [156]
3 years ago
10

Help me please i wish i can get somehelp

Mathematics
1 answer:
USPshnik [31]3 years ago
4 0

Answer:

29. \frac{1}{3}

30. a) 32

b) Yes, the ratio will change 1 : 2.

Step-by-step explanation:

<em>Question 29.</em>

Given that:

Number of gold medals won by France = 11

Number of silver medals won by France = 9

Number of bronze medals won by France = 13

To find:

The ratio of gold medals won to the total number of medals won by France.

Solution:

First of all, we need to find the total number of medals won by France.

Total number of medals won = 11 + 9 + 13 = 33

The required ratio can be found as:

\dfrac{\text{Number of gold medals won}}{\text{Total number of medals won}}\\\Rightarrow \dfrac{11}{33}\\\Rightarrow \bold{\dfrac{1}{3}}

<em>Question 30:</em>

Number of girls = 20

Ratio of boys to Ratio of girls = 3 : 5

a. Total number of students in the class?

First of all, we need to find the number of boys in the class then we will add the value to the number of girls to get the answer.

Let the number of boys = x

As per the ratio, we can write:

\dfrac{3}{5 } = \dfrac{x}{20}\\\Rightarrow x = 12

Total number of students = 20 + 12 = <em>32</em>

b. Four number of boys and four girls are moved to other class.

Number of boys left = 12 - 4 = 8

Number of girls left = 20 - 4 = 16

New ratio = 8 : 16 = <em>1 : 2</em>

Therefore, the ratio got changed to <em>1 : 2</em>.

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Answer:

t=\frac{7.2-8}{\frac{2.1}{\sqrt{41}}}=-2.439    

p_v =P(t_{(40)}  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is lower than 8 ppb at 1% of signficance. We need to be careful with this interpretation since the p value is near to the significance level.  

Step-by-step explanation:

Data given and notation  

\bar X=7.2 represent the mean height for the sample  

s=2.1/tex] represent the sample standard deviation [tex]n=41 sample size  

\mu_o =8 represent the value that we want to test

\alpha=0.01 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

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

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is less than 8, the system of hypothesis would be:  

Null hypothesis:\mu \geq 8  

Alternative hypothesis:\mu < 8  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{7.2-8}{\frac{2.1}{\sqrt{41}}}=-2.439    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=41-1=40  

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

p_v =P(t_{(40)}  

Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is lower than 8 ppb at 1% of signficance. We need to be careful with this interpretation since the p value is near to the significance level.  

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