1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ankoles [38]
3 years ago
13

Confidence Interval Mistakes and Misunderstandings—Suppose that 500 randomly selected recent graduates of a university were as

ked to rate the school’s academic advising services on a scale from 1 to 10. The sample mean rating was found to be 8.6. Assume that the population standard deviation is known to be 2.2
A.) Someone computes the 95% confidence interval for the average satisfaction score as 8.6 ± 1.96(2.2). What is the mistake of this student?

B.) After correcting the mistake in part (A), the student states "I am 95% confident that the sample mean rating falls between 8.4 and 8.8." What is wrong with this statement?

C.) The student quickly realizes the mistake made in part (B) and now says "The probability that the true mean rating is between 8.4 and 8.8 is 95%." What misinterpretation is the student making now?

D.) Finally, to defend the use of the Normal distribution to calculate the confidence interval the student says, "Because the sample size is quite large, the population of alumni ratings will be approximately Normal." Correct this misunderstanding.
Mathematics
1 answer:
kvv77 [185]3 years ago
7 0

Answer:

The correct 95% confidence interval is (8.4, 8.8).

Step-by-step explanation:

The information provided is:

n=500\\\bar x=8.6\\\sigma=2.2

(a)

The (1 - <em>α</em>)% confidence interval for population mean (<em>μ</em>) is:

CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}

The 95% confidence interval for the average satisfaction score is computed as:

8.6 ± 1.96 (2.2)

This confidence interval is incorrect.

Because the critical value is multiplied directly by the standard deviation.

The correct interval is:

8.6\pm 1.96 (\frac{2.2}{\sqrt{500}})=8.6\pm 0.20=(8.4,\ 8.6)

(b)

The (1 - <em>α</em>)% confidence interval for the parameter implies that there is (1 - <em>α</em>)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence interval for the mean rating, (8.4, 8.8) implies that the true there is a 95% confidence that the true parameter value is contained in this interval.

The mistake is that the student concluded that the sample mean is contained in between the interval. This is incorrect because the population is predicted to be contained in the interval.

(c)

The (1 - <em>α</em>)% confidence interval for population parameter implies that there is a (1 - <em>α</em>) probability that the true value of the parameter is included in the interval.

The 95% confidence interval for the mean rating, (8.4, 8.8) implies that the true mean satisfaction score is contained between 8.4 and 8.8 with probability 0.95 or 95%.

Thus, the students is not making any misinterpretation.

(d)

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

In this case the sample size is,

<em>n </em>= 500 > 30

Thus, a Normal distribution can be applied to approximate the distribution of the alumni ratings.

You might be interested in
What is 24.012 divided by 6 with the work
AURORKA [14]
So you pretty much divide 24 by 6, getting you the 4 up top. Then you add your decimal place and put up two zeroes. Once you put 12 down it can be divided by 2. Getting you’re finally answer 4.002. Hope that helps.

8 0
3 years ago
127°<br> 37°<br> Х<br> Calculate the size of angle x.<br> angle x =
Andrei [34K]

Angle is not visible mate

!!!!!!!!!!!

5 0
2 years ago
the members of the band are selling raffle tickets.if their goal is to raise at least $950,the number of tickets they must sell
Diano4ka-milaya [45]

140 is the solution of the inequality

Step-by-step explanation:

The inequalities are used just like equations.

Given

Total amount to be raised = $950

Price of one ticket = $2.50

The inequality that represents the situation is:

2.50x≥950

Dividing both sides by 2.50

\frac{2.50x}{2.50} \geq \frac{950}{2.50}\\x\geq 140

140 is the solution of the inequality

Keywords: Inequality, cost

Learn more about inequalities at:

  • brainly.com/question/13219835
  • brainly.com/question/1836777

#LearnwithBrainly

3 0
3 years ago
Ten weeks of data on the Commodity Futures Index are as follows.
IgorLugansk [536]

The analysis of time series is a process by which a set of observations in a time series is analyzed.

Part a: The time series plot is constructed both in de$mo$ and excel sheet.

b. The data appear to follow a horizontal pattern.

Part b: The trial and error is used to find the value of exponential smoothing coefficient that results in MSE= 0.009 which is less than 0.01.

The MSE in the first table is calculated using the average of the two previous years.

The MSE in the second table is calculated using the moving average

The MSE in the third table is calculated by using ∝= 0.4 and the value of alpha changes to different values as shown in the cell U20, V20 and W20.

The MSE is the mean squared error.

We find the error by subtracting <u><em>forecast</em></u> data from the <em><u>actual</u></em> data.

The forecasted data may be average of 2 years , moving average of 3 years or adding the multiplied chosen value of alpha with the actual data and the multiplied value of 1- ∝ with the forecasted value of data.

The error is then squared.

The squared error is then averaged which gives the MSE.

The values of ∝= 0.400641005, 0.40319659, 0.400641001 may give the best MSE values.

brainly.com/question/24149197

brainly.com/question/20376850

brainly.com/question/15875267

Download xlsx
<span class="sg-text sg-text--link sg-text--bold sg-text--link-disabled sg-text--blue-dark"> xlsx </span>
695db9f7774343e86b7416fee987c7ea.png
8 0
2 years ago
1/4z-2/7=5/7 what is z
Alenkasestr [34]

Answer:

z=4

Step-by-step explanation:

1/4z-2/7=5/7

1/4z= 5/7+2/7

1/4z=1

z=4

3 0
3 years ago
Other questions:
  • a passenger train leaves a train depot 2.5 after a freight train leaves the same depot the passenger train is traveling 13 mph f
    5·1 answer
  • On a scale drawing of a dock for a marina, 1 inch equals 15 feet. the dock is 200 feet long. what is the length of the dock on t
    10·1 answer
  • You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers &amp
    10·2 answers
  • A randomly selected sample of college basketball players has the following heights in inches. See Attached Excel for Data. Compu
    13·1 answer
  • I WANT TO KNOW<br> WHAT IS THE MULTIPLE OF 6
    12·1 answer
  • How many 1/4 hours are in a 1 hour
    6·2 answers
  • And here are the answer choices
    14·2 answers
  • Addison has 124,234,281,284 cartons of milk, she dropped like 456,789,098,345,678,987,654,568 of them, how many did bruh bruh br
    11·2 answers
  • Please help me out on this..............
    9·1 answer
  • Name the multiplication property shown the equation 12 m=m . 12
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!