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bija089 [108]
3 years ago
14

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seeding. Use a hydroponics grow proce

dure that utilized water containing the nutrient, they planted 6 tomato plants and recorded the heights of each plant 14 days after germination. those heights were 54.2, 59.8, 61.8, 63.3, 65.1, 71.4
Use technology, find the 95% confidence interval for the population mean.

use technology, construct a 99% confidence interval.
Mathematics
1 answer:
Rashid [163]3 years ago
8 0

Answer:

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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Step-by-step explanation:

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  105.25

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You have some turtles and some pelicans. Together there are 114 legs and a total of 34 animals. How many of each animal are ther
Ann [662]

Let t and p represent the numbers of turtles and pelicans, respectively.

... 2p + 4t = 114 . . . . . . . the number of legs is 114

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Divide the first equation by 2 and subtract the second.

... (2p +4t)/2 - (p +t) = (114)/2 - 34

... t = 23 . . . . . . . . . . . . . . . . . . . . . . simplify

Then p = 34 - t = 11

There are 11 pelicans and 23 turtles.

_____

You can get to the same answer by considering the number of legs you would have if all the animals were pelicans. That would be 34*2 = 68. The is 46 fewer legs than there actually are. Each turtle that replaces one of those 34 pelicans adds 2 legs to the total, so to add 46 legs, we must replace 46/2 = 23 pelicans with turtles. That is, there are 23 turtles and 11 pelicans.

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Patty made a banner that has an area of 175 square inches. The length and width of the banner are whole numbers. The length is 7
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Answer:

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6 0
2 years ago
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