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Margarita [4]
3 years ago
13

A factory produces c cans of paint in h hours according to the equation c= 50h. What represents the unit rate of cans produced p

er hour?
Mathematics
1 answer:
Marat540 [252]3 years ago
6 0
50 cans are made per hour
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The 95% confidence interval for the mean would be given by (56.604;68.596)

The 99% confidence interval for the mean would be given by (53.196;72.004)

Step-by-step explanation:

1) Previous concepts

When we compute a confidence interval for the mean, we are interested on the parameter population mean, and we use the info from the sample to estimate this parameter.

2) Basic operations

The sample mean can be calculated with the following formula

\sum_{i=1}^n \frac{x_i}{n}

Using excel we can use this function to calculate the mean:

=AVERAGE(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is \bar X=62.6

In order to find the sample deviation we can use this formula

s=\sqrt{\sum_{i=1}^n \frac{(x_i-\bar X)^2}{n-1}}

And using excel we can use this function to calculate the sample standard deviation:

=STDEV.S(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is s=5.713

The sample size for this case is n=6, n<30 so then is better use the t distribution to calculate the margin of error. First we need to calculate the degrees of freedom, on this case df=n-1=6-1=5

The formula for the confidence interval would be given by:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

3) Part a

If we want a 95% or 0.95 of confidence, then the value for the signficance is \alpha=1-0.95=0.05, and \alpha/2=0.025, and 1-\frac{\alpha}{2}=0.975 so we can find the critical t value with the following formula in excel:

=T.INV(0.975,5)

And we got t_{\alpha/2}= 2.571

And we can replace into equation (1) and we got:

62.6 \pm 2.571\frac{5.713}{\sqrt{6}}

And using excel with the following formulas we got:

=62.6-2.571*(5.713/SQRT(6)) = 56.604

=62.6+2.571*(5.713/SQRT(6)) = 68.596

So the 95% confidence interval for the mean would be given by (56.604;68.596)

4) Part b

If we want a 99% or 0.99 of confidence, then the value for the signficance is \alpha=1-0.99=0.01, and \alpha/2=0.005, and 1-\frac{\alpha}{2}=0.995 so we can find the critical t value with the following formula in excel:

=T.INV(0.995,5)

And we got t_{\alpha/2}= 4.032

And we can replace into equation (1) and we got:

62.6 \pm 4.032\frac{5.713}{\sqrt{6}}

And using excel with the following formulas we got:

=62.6-4.032*(5.713/SQRT(6)) = 53.196

=62.6+4.032*(5.713/SQRT(6)) = 72.004

So the 99% confidence interval for the mean would be given by (53.196;72.004)

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Yeah i think it’s uh i think it’s a correct
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