"What are the correct notations for both the population parameter and the sample statistic for the following: mean and proportion? What distribution is appropriate for use with each parameter (assume the populations are normally distributed and the sample is small for the mean)? What is the formula for the test statistic when testing these parameters?"

a) Parameters :-

The statistical constants of the population namely mean 'μ' and variance σ²

are referred to as parameters.

b Statistics:-

The statistical computed from sample observations mean (x⁻) and variance

(S² ) are usually referred as statistics

c) the test statistic

Step-by-step explanation:

Explanation:-

Population:-

Population consists of the totality of the observations with which we are concerned. This number is finite or infinite.

The number of observations in the population is defined to be the size of the population.

Sample:-

A sample is a subset of a population

Parameters :-

The statistical constants of the population namely mean 'μ' and variance σ²

are referred to as parameters.

Statistics:-

The statistical computed from sample observations mean (x⁻) and variance

(S² ) are usually referred as statistics

Central limit theorem:

If x⁻ is the mean of a random sample of size n taken from a population with mean 'μ' and finite variance σ² , then the limiting form of the distribution

Z- distribution:-

Suppose we want to test whether the given sample of size n has been drawn from a population with mean ''μ'

we set up null hypothesis that there is no significance between  sample mean x⁻  and mean 'μ ' then The test statistic

standard deviation of the population parameter σ and sample statistic mean x⁻

Z- distribution for the given single proportion

Suppose we want to test whether the given sample of size n has been drawn from a normal population.

we set up null hypothesis that there is no significance between  sample proportion 'p' and Population proportion 'P' then The test statistic

Q =1-P

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!