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Anastasy [175]
3 years ago
9

If {a_{n}} and {b_{n}} are geometric sequences with common ratios of r₁ and r₂, is {a_{n}b_{n}} a geometric sequence too? If yes

, what is the common ratio?
Mathematics
1 answer:
MissTica3 years ago
4 0
A_{n+1}b_{n+1} / a_{n}b_{n} =( a_{n+1} /  a_{n}) * (  b_{n+1} /  b_{n} ) = ( r1 ) * ( r2) =>
{a_{n}b_{n}} a geometric sequence;  the common ratio is  ( r1 ) * ( r2) .
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In a recent poll, 370 people were asked if they liked dogs, and 7% said they did. Find the margin of error of this poll, at the
Dennis_Churaev [7]

Answer:

ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p represent the real population proportion of interest

\hat p=0.07 represent the estimated proportion for the sample

n=370 is the sample size required (variable of interest)

z represent the critical value for the margin of error

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})  

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.90=0.10 and \alpha/2 =0.05. And the critical value would be given by:  

z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64  

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}} (a)  

And replacing into formula (a) the values provided we got:

ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218

The margin of error on this case would be ME=0.0218

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Is the percentage of the variation in the dependent variable that results from the independent variable?
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<u>Number of attempts:  </u>

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<u>Answer: </u>130 times

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