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3 years ago

In a class of 23 student the girls were 7 more than the boys how many boys were in the class

Mathematics

1 answer:

Softa [21]3 years ago

5 0

Answer:

x=# of boys

x+7=# of girls

x+x+7=25

2x+7=25

2x=25-7

2x=18

x=18/2

x=9 boys

x+7=16 girls

If you don't understand variables use trial and error.

Boys Girls

1 8

2 9

3 10

4 11

5 12

6 13

7 14

8 15

9 16 9+16=25 students

You could start this way...

Boys Girls

12 13

11 14

10 15

9 16 16 is 7 more than 9

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So on this case the 95% confidence interval would be given by (25.06;33.74)

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Data given: 30 30 42 35 22 33 31 29 19 23
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$\mu$ population mean (variable of interest)

$\sigma=7$ represent the population standard deviation

n=10 represent the sample size

95% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$29.4-1.96\frac{7}{\sqrt{10}}=25.06$

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What are H0 and Ha for this study?

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The statistic for this case is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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".

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

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Give the appropriate conclusion for the test

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3 0

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In a class of 23 student the girls were 7 more than the boys how many boys were in the class​

In a class of 23 student the girls were 7 more than the boys how many boys were in the class