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2 years ago

Dale says the ratios 3:5 and 2:10 are equivalent. Is He correct? Explain

Mathematics

1 answer:

Mnenie [13.5K]2 years ago

3 0

Answer:

No, Dale Isn't correct because 3:5 is greater than 2:10

Step-by-step explanation:

3:5 and 2:10 is the same as in $\frac{3}{5}$ and $\frac{2}{10}$

First Find the least common denominator or LCM of the two denominators:

LCM of 5 and 10 is 10

Next, find the equivalent fraction of both fractional numbers with denominator 10

For the 1st fraction, since 5 × 2 = 10,

$\frac{3}{5} =\frac{3*2}{5*2} =\frac{6}{10}$

Likewise, for the 2nd fraction, since 10 × 1 = 10,

$\frac{2}{10} =\frac{2*1}{10*1} =\frac{2}{10}$

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

$\frac{6}{10} >\frac{2}{10} Or\frac{3}{5} >\frac{2}{10}$

Hence, $\frac{3}{5}$ is <u>Greater than </u> $\frac{2}{10}$

Hence, 3:5 is <u>Greater than </u>2:10

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spin [16.1K]

Answer:

$z=\frac{0.18 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=2.67$

Step-by-step explanation:

1) Data given and notation

n=100 represent the random sample taken

X=18 represent the ounce cups of coffee that were underfilled

$\hat p=\frac{18}{100}=0.18$ estimated proportion of ounce cups of coffee that were underfilled

$p_o=0.1$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion it's higher than 0.1 or 10%:

Null hypothesis: $p\leq 0.1$

Alternative hypothesis: $p > 0.1$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.18 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=2.67$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level assumed for this case is $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a one right tailed test the p value would be:

$p_v =P(Z>2.67)=0.0037$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance thetrue proportion is not significanlty higher than 0.1 or 10% .