Answer:
Step-by-step explanation:
Answer:
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
Critical value at 90% confidence = 1.645
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $79.20
Standard deviation r = $10.41
Number of samples n = 14
Confidence interval = 90%
Using the z table;
The critical value that should be used in constructing the confidence interval.
z(α=0.05) = 1.645
Critical value at 90% confidence z = 1.645
Substituting the values we have;
$79.20+/-1.645($10.42/√14)
$79.20+/-1.645($2.782189528308)
$79.20+/-$4.576701774067
$79.20+/-$4.577
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
A) In order to create a sampling plan, you need to follow the following 5 steps:
1) Define the sample population: who are the customers you want to contact?
The costumers who bought a new car on a certain year.
2) Define the size of population: how many customers are you going to contact?
Of the 30000 customers who bought a car, you want to contact 1000 customers.
3) Define the contact options: how are you going to contact the customers?
You have a list of names and addresses, therefore you can send a questionnaire via mail.
4) Form a sampling frame: what is the time or contact frame to get in touch with your customers?
You will send the questionnaires and you will wait two months for the answer.
5) Define the analysis method: is yours a qualitative or quantitative research?
In your case, you want a quantitative research and therefore a probabilistic sampling.
B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.
C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
P = 13 / 1000
= 0.013
Therefore,
N = <span>0.013 </span>× 30000
= 390
Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.
I'll explain how to do the first one:-
y = cos-1(x2)
This can be described as ' a function of a function' x^2 is a function of x and cos-1(x^2) is a function of x^2.
We need to apply the chain rule.
Personally I find this easier to understand if i let u = x^2, so
If y = f(u) and u is a function of x then
dy/dx = dy/ du * du/dx
Here u = x^2 and y = cos-1(u)
du/dx = 2x
so dy/dx = d(cos-1(x^2) dx = dy/du * du/dx
= -1 / √(1 - u^2) * 2x
= -2x / √(1 - u^2)
= -2x / √(1 - (x^2)^2)
= -2x / √(1 - x^4)
I hope this helps. but if not. you might like to employ the formulae in the question - The square boxes contain the 'u' s in my answer. These formulae are equivalent to my explanation.
