Dr. Scott wants to know the true average cost of educational materials for stude

Question

Dr. Scott wants to know the true average cost of educational materials for students at Texas College. A recent survey asked the question, "How much money (in dollars) did you spend on textbooks and course-required materials this semester?"

Using only the data provided (at bottom) from the survey answer the following questions.

Question 1:

(a) Which one value is your best estimate of the true average cost of educational materials for students at Texas College?

(b) Is it likely that your answer to question 1(a) is the exact value of the true average? Explain using complete sentences.

Question 2:

Between which values is the average cost of educational materials for students at Texas College likely to fall? Show all work including any Excel functions used.

Question 3:

How confident are you in this answer? Explain what this means to someone who has never heard of confidence in statistics.

Question 4:

How would your answer to question 2 change if you were given twice as many data points? Explain using complete sentences.

Question 5:

(a) Dr. Scott believes that the true average cost of educational materials for students at Texas College is $175. Does this agree or disagree with your answer?

(b) Is it likely that Dr. Scott is correct? Explain using complete sentences.

(c) Is it possible that Dr. Scott is correct? Explain using complete sentences.

A recent survey asked the question, "How much money (in dollars) did you spend on textbooks and course-required materials this semester?" The results of the survey are given below. 200 200 200 600 300 300 380 500 800 500 0 400 750 400 0 90 400 200 300 550 397 200 200 500 400 250 750 275 378 200 200 980 120 300 500 400 300 150 500 300 809 300 300 300 75 0 500 700 350 1100 478 300 300 800 600 300 0 600 500 600 400 450 800 340 300 800 400 350

Explanation / Answer

Here sample size n = 68

Question 1

(a) Here the avergae value is the best estimate of the  true average cost of educational materials for students at Texas College

which is x = $ 398.85

(b) Yes, the true average will likely be the best estimate of true average cost it is because the mean value is equidistant to all the datapoints of the distribution

Question 2

Here the value is most likely to fall in between mean +- Z95% * standard deviation = x +- 1.96 se0

Where standard deviation s = 235.31 calculated by using formula [STDEV ()]

Standard error of sample mean se0 = s/sqrt(n) = 235.31/sqrt(68) = 28.536

so the value which is most likely are = 398.85 +- 1.96 * 28.536 = ($ 342.92, $ 454.78)

Question 3. Here we are 95% confident about this thing.

To a laymen, we can explain that if we take samples of size 68 from the population through random sampling, approximately 19 out of 20 times, we will get our average cost of study materials between these two values.

Question 4

If we are given twice the data points, out confidence interval will be reduced by sqrt(2) times, as standard error of mean is inversely proportional to sample size. In laymen terms the confidence interval will get reduced by 30%.

Question 5

(a) Here the confidence interval of 95% if far greater than $175 so we reject the Dr. Scott assumption.

(b) No,it is not likely that Dr. scott is correct as their is very small probability of 0.001 that he may be correct.

(c) Yes, it is possible, the probability of such event is very low but it is not absolutely zero,

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.