Mathematics, 29.10.2020 16:30 grugfhb

The contents of seven similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8,10.0, 10.2, and 9.6 liters. Find a 95% confidence interval for the mean contents of all such containers, assuming an approximately normal distribution. (Round your answers into two decimal places.)

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Answer from: avasteinhebel10

The 95 confidence interval is $9.738 < \mu < 10.262$

Step-by-step explanation:

The sample size is n = 7

The sample data is 9.8, 10.2, 10.4, 9.8,10.0, 10.2, and 9.6 liters

Generally the sample mean is mathematically represented as

$\= x = \frac{\sum x_i }{n }$

=> $\= x = \frac{ 9.8 + 10.2 + 10.4 +\cdots + 9.6}{7 }$

=> $\= x = 10$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum ( x_i - \= x)^2 }{n-1} }$

=> $\sigma = \sqrt{\frac{ ( 9.8 - 10)^2 + ( 10.2 - 10)^2+ \cdots + ( 9.6 - 10)^2}{7-1} }$

=> $\sigma =0.283$

Note : We are making use of t distribution because n is small i.e n < 30

Generally the degree of freedom is mathematically represented as

df = n - 1

=> df = 7 - 1

=> df = 6

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the t distribution table the critical value of at a degree of freedom of is

$t_{\frac{\alpha }{2}, 6 } = 2.447$

Generally the margin of error is mathematically represented as

$E = t_{\frac{\alpha }{2} , 6} * \frac{\sigma }{\sqrt{n} }$

=> $E = 2.447 * \frac{0.283}{\sqrt{7} }$

=> E = 0.262

Generally 95% confidence interval is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $10 -0.262 < \mu$

=> $9.738 < \mu < 10.262$

Answer from: Quest

step-by-step explanation:

Answer from: Quest

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

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The contents of seven similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8,10.0, 10.2, and 9...