Question

A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.

Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.

Answer 1

Ans: 2*ME = 80%-6% = 72%
ME = 36%
----------- -------
Calculate the confidence interval and explain what it means in terms of the situation.
90% CI:: 0.06 < p < 0.80
We have 90% confidence the population proportion is between 6% and 80%

Answer 2

Need more explanation?

Answer 3

Or are you good?

Answer 4

Where did you get 0.06% and 0.80% from?

Answer 5

What does "nine times out of ten" tell you?

Answer 6

That is the confidence interval right? 90%

Answer 7

good

Answer 8

What are the critical values for a 90% confidence interval?

Answer 9

The critical value is 1.645

Answer 10

Correct, so Zα/2=Z.05=1.645. (Don't worry about the notation if you haven't seen it before.)

The margin of error is given to be 5%, or 0.05, since an average score is expected to fall within 5% of the estimated mean.

The estimated mean itself is?

Answer 11

it should be a very small percentage

Answer 12

it should be a very small percentage

Answer 13

Thats where I get stuck, so the margin of error is 0.05 which answers part of the problem, but what do you mean by the estimated mean itself?

Answer 14

is there another formula?

Answer 15

5% is correct

Answer 16

Okay, all i really need is the final part,Calculate the confidence interval and explain what it means in terms of the situation.

Answer 17

If you can help me solve that, I'll be good

Answer 18

(x¯−Zα/2σ2n−−−√, x¯+Zα/2σ2n−−−√)

x¯ is the estimated average score. According to the given info, that would be 75%, or 0.75.

The exam creator says the scores will fall within 5% of a 75% score, so the margin of error is 5%, or 0.05. In the formula, σ2n−−−√ is the margin of error.

The critical value for a 90% confidence interval is 1.645, so Zα/2=1.645.

So to reiterate, the confidence interval would be
(0.75−1.645×0.05, 0.75+1.645×0.05)

Simplify.

Answer 19

Can you help me simplify? would it be ( -0.04475 , 0.83225)? and what does it tell us?

Answer 20

Those are what i got

Answer 21

Your answer would be the interval, yes. I suggest you study up on the topic. It doesn't seem like you're really grasping the procedure here.

Answer 22

Can you tell me what the interval means?

Answer 23

a space between things, points, limits, etc.: an interval of ten. 4. Math. a. the totality of points on a line between two designated points or endpoints that may or may not be included. b. any generalization of this to higher dimensions, as a rectangle with sides parallel to the coordinate axes

Answer 24

alright thanks, ill give you the best response even though you just copied and pasted the same exact thing, and even copied the wrong problem lmao

Answer 25

Note that the question asks for the meaning of the confidence INTERVAL ( not the confidence level ) in the situation presented. A confidence interval gives the likely range for a population parameter based on sample information. This interval is formed using the standard normal probability distribution, assuming that the sample size was 30 or greater. In the given situation we can say that a 90% confidence interval for the average score of the population is (75.2%, 84.8%) and 90% of such intervals will contain the average score of the population.

Answer 26

A little pointer!
Good luck!!