Question

statistics, how to knoe if its not a normal distribution.. pls see attachment

Answer 1

see attachment

Answer 2

Before even looking at the data, we know that the distribution of class sizes could
not possibly be normal. Explain why.

Answer 3

@kropot72

Answer 4

I want to know this too.

Answer 5

The standard deviation is too large for the distribution to be normal. In the case of a normal distribution almost all the data points are within plus and minus 3 standard deviations of the mean. Using the given data what is the value of the mean minus 3 standard deviations?
33.73 - (3 * 18.50) = ?

Answer 6

sorry i dont really understand , they said that before even looking at the data.. so does it mean i shouldnt look at any of the data give, just read from the quesiton and make a conclusion ?

Answer 7

*given

Answer 8

the answer is -21.77.. but why did u minus the mean with 3 std.dev?

Answer 9

The mean and the standard deviation are not data, they are both a statistic. Getting a negative answer shows that it is not possible for all the data points to be within plus and minus 3 standard deviations of the mean. This conclusion is evident without having to look at the data.

Answer 10

okay thank you.. i understand now.. sorry but why do we have to take 3 to multiply for the standard deviation? why cant it be 2 or 4? sorry

Answer 11

The empirical rule applying to a normal distribution states that approximately 99.7% of the data points lie within the range of plus and minus 3 standard deviations of the mean. We checked using the statistics 'the mean' and 'the standard deviation' to see if data could exist at the mean minus 3 standard deviations and got a negative result. But the number of students per class cannot be negative. Therefore the distribution of the data cannot be normal and we know this without knowing the details of the data.

Answer 12

okay thank alot for the explanation.... but why is it still appropriate for us to use inference methods which rely on the assumpyion of normality?

Answer 13

Inference in statistics is drawing conclusions about a parent population on the basis of evidence obtained from a sample. If the evidence from a sample justifies the assumption of the parent population being normal, it is often valid to use the powerful techniques that have been developed for the normal distribution.

Answer 14

ok thanks.. so for this question.. how can we know that the evidence from sample justifies the assumption of the parent population being normal?

Answer 15

Do you know the Central Limit Theorem?

Answer 16

yup as n increases, the sampling distribution of x approaches a normal distribution

Answer 17

If samples of size n are taken from a parent population with mean 'mu' and standard deviation 'sigma', then the distribution of their means is approximately normal, with
\[Mean=\mu\]
and
\[Standard\ deviation=\frac{\sigma}{\sqrt{n}}\]
Note: I have to have a meal now, but I can help later if you need it.

Answer 18

oh okay so because its approximately normal, so u willbe able to use the inference? okay thank you! enjoy your meal

Answer 19

If the sample size is equal to 30 or greater than 30, then by the Central Limit Theorem the mean of the underlying population can be estimated by Statistical Inference even if the distribution of the underlying population is not normal. The confidence interval for the mean is given as
\[\bar{x}-z\frac{\sigma}{\sqrt{n}}<\mu<\bar{x}+z\frac{\sigma}{\sqrt{n}}\]
where
x-bar is the sample mean
z is 1.645 to find a 90% confidence level
1.960 to find a 95% confidence level
2.576 to find a 99% confidence level
sigma is the population standard deviation

Answer 20

alright thanks alot! i not understand the concept :) and also one more question.. if we were to conduct a hypothesis test, at the 10% level of signigicance, to determine if there is a difference in effectiveness between the old formula( 0.7) and new formula(0.76). is the alternative hypothesis gonna be not equals to more than 0.7?

Answer 21

*i now

Answer 22

Can you please post the full question regarding testing a hypothesis. I need more information to give you an answer.

Answer 23

sorry wrong atachment

Answer 24

The null hypothesis is that the effectiveness is equal to 0.7.
The alternative hypothesis is that the effectiveness is not equal to 0.7.
In this case a two-tail test is needed.

Answer 25

okay thank you!!

Answer 26

You're welcome :)