Please answer the bushfire question!

Statistics

EastWind [94]

$\frac{986}{1700} = 0.58$

$0.58 * 100=58$

The company has a 58% success rate.

5 0

3 years ago

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Todd can run 1/2 a mile in 1/12 of an hour. what is todd’s rate in miles per hour?

stiks02 [169]

If he runs 1/2 a mile in 5 minutes then 60 minutes would be 5x12 and 1/2x12 would be 6 so he can run 6 miles per hour

7 0

3 years ago

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How can simple interest make saving money easier?

Lyrx [107]

Answer:

Your answer is b

4 0

3 years ago

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How to find the value of each power

Inessa [10]

Exponent of a number says how many times.

2³

The 2 is the base number, while the little 3 is the exponent.

2³ = 2 x 2 x 2 = 8

Basically, you would just have to do two, three times.

Very time when you get the hang of it !!

4 0

3 years ago

5. Decide if each of the following statements is true or false. Explain your reasoning in each case.

sertanlavr [38]

Answer:

a. The smaller the sample size, the smaller the margin of error.

False if we see the value for the sample size is on the denominator and if we decrease the value of n then increase the value for the margin of error since the margin of error and the sample size are inversely proportional, with the estimated proportion and the confidence level fixed values.

b. If the margin of error is 0.05 and the observed proportion of red chips is 0.45, then the true population proportion is likely to be between 0.40 and 0.50.

Correct. The confidence interval for the population proportion is given by:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

Or equivalently:

$\hat p \pm ME$

And if we replace on this case we got:

$0.45-0.05=0.40$

$0.45 +0.05=0.50$

So then the true proportion is between 0.4 and 0.5 for this case.

Step-by-step explanation:

Previous concepts

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".

Solution to the problem

The population proportion have the following distribution

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

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)

Now if we analyze the statements one by one we have this:

a. The smaller the sample size, the smaller the margin of error.

False if we see the value for the sample size is on the denominator and if we decrease the value of n then increase the value for the margin of error since the margin of error and the sample size are inversely proportional, with the estimated proportion and the confidence level fixed values.

b. If the margin of error is 0.05 and the observed proportion of red chips is 0.45, then the true population proportion is likely to be between 0.40 and 0.50.

Correct. The confidence interval for the population proportion is given by:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

Or equivalently:

$\hat p \pm ME$

And if we replace on this case we got:

$0.45-0.05=0.40$

$0.45 +0.05=0.50$

So then the true proportion is between 0.4 and 0.5 for this case.

4 0

4 years ago