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
olga_2 [115]
3 years ago
12

Many people now turn to the Internet to get information on health-related topics. A research article used Flesch reading ease sc

ores (a measure of reading difficulty based on factors such as sentence length and number of syllables in the words used) to score pages on Wikipedia and on WebMD. Higher Flesch scores correspond to more difficult reading levels. The paper reported that for a representative sample of health-related pages on Wikipedia, the mean Flesch score was 26.6 and the standard deviation of the Flesch scores was 14.7. For a representative sample of pages from WebMD, the mean score was 43.6 and the standard deviation was 19.3. Suppose that these means and standard deviations were based on samples of 40 pages from each site.
Required:
a. Construct a 90% confidence interval estimate of the difference in mean Flesch reading ease score for health-related pages on Wikipedia and health-related pages on WebMD.
b. What does this confidence interval imply about the readability of health related information from these two sources?
Mathematics
1 answer:
romanna [79]3 years ago
6 0

Answer:

a) The 90% confidence interval estimate of the difference in mean Flesch reading ease score for health-related pages on Wikipedia and health-related pages on WebMD = (-23.46, -10.54)

b) Since the confidence interval for possible difference in the population mean Flesch score for health related issues for the two websites doesn't contain a 0. It means there is a significant difference between the mean Flesch score for health related issues on WebMD websites and Wikipedia websites.

Specifically, the confidence interval obtained, being all negative, shows that the population mean Flesch score for health related issues on Wikipedia websites is lower than that of WebMD pages. This further indicates that it is easier to read health related issues on Wikipedia websites than health related issues on WebMD websites according to the range of values that the population mean difference in Flesch score for both sites can take on.

Step-by-step explanation:

When independent distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

For a difference in data distribution of the pages, the new distribution would be

X₁ - X₂

X₁ = Distribution for Flesch reading ease score for health-related pages on Wikipedia

X₂ = Distribution of Flesch reading ease score for health-related pages on WebMD

λ₁ = 1

λ₂ = -1

μ₁ = 26.6

μ₂ = 43.6

σ₁² = 14.7² = 216.09

σ₂² = 19.3² = 372.49

Combined mean difference = Σ λᵢμᵢ

= (1×26.6) + (-1×43.6) = -17

Combined variance = Σ λᵢ²σᵢ²

= (1²×216.09) + [(-1)²×372.49) = 588.58

Combined standard deviation = √(variance)

= √588.58 = 24.26

Confidence Interval for the population mean difference is basically an interval of range of values where the true population mean difference can be found with a certain level of confidence using the information from the sample provided.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean difference = -17

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 40 - 1 = 39.

Significance level for 90% confidence interval

(100% - 90%)/2 = 5% = 0.05

t (0.05, 39) = 1.685 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 24.26

n = sample size = 40

σₓ = (24.26/√40) = 3.836

90% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = -17 ± (1.685 × 3.836)

CI = -17 ± 6.46366

90% CI = (-23.46366, -10.53634)

90% Confidence interval = (-23.46, -10.54)

b) Since the confidence interval for possible difference in the population mean Flesch score for health related issues for the two websites doesn't contain a 0. It means there is a significant difference between the mean Flesch score for health related issues on WebMD websites and Wikipedia websites.

Specifically, the confidence interval obtained, being all negative, shows that the population mean Flesch score for health related issues on Wikipedia websites is lower than that of WebMD pages. This further indicates that it is easier to read health related issues on Wikipedia websites than health related issues on WebMD websites according to the range of values that the population mean difference in Flesch score for both sites can take on.

Hope this Helps!!!

You might be interested in
Five points are plotted on a cm grid.The 5 points are 5 vertices of a hexagon. Each side of the hexagon has the same length.Work
Eddi Din [679]

Answer:

(13, 5)

Step-by-step explanation:

6 0
2 years ago
Please help!! Problem in picture
notsponge [240]
20.if m <6=72, then m < 7=108
21. if m<8,then m<7=80
22.if m<110,then m<6=90
23.if m<123, then m<8=123
24.if m<142, then m<7=38
25.if m<13, then m<8=167
26.if m<170, then m<10
27.if m<26, then m <154
,
3 0
2 years ago
A cone has a volume of 226.08 cubic millimeters and a height of 6 millimeters. What is its
dezoksy [38]

Answer:

r≈5.36656314

Step-by-step explanation:

Since A=πr(r+\sqrt{h^2+r^2}) so we get that 226.08/pi≈72 or 226.08/3.14=72 we then plug it in to get 72=r(r+\sqrt{36+r^2}) so we get r≈5.36656314

6 0
3 years ago
Read 2 more answers
Solve x2 + 4x + 8 = 0.
Novosadov [1.4K]
X^2 + 4x + 8 = 0
( x + 2 ) ( x + 2 ) = 0

i am a mathematics teacher. if anything to ask please pm me
5 0
3 years ago
Help me please please please
avanturin [10]

Answer:

3.33lbs. repeating?

Step-by-step explanation:

I think it would just be 10/3 and be 3.33333333 and so on. (im just taking a guess)

3 0
2 years ago
Other questions:
  • Distance versus time is plotted and a best-fit line is found to be y= 0.098 x+ 0.01. what are the units of the slope 0.098?
    11·1 answer
  • The graph shown corresponds to someone who makes
    14·1 answer
  • Ansel works on commission as a furniture salesman. He sold a couch that cost $800 and received a $120 commission. What percent o
    10·2 answers
  • Carson bought a coat for 40% of the original price, then another 15% off the discounted price. If the coat originally cost $149,
    15·1 answer
  • A small Fruit smoothie is 18 ounces why a large fruit smoothie is 21.96 ounces the large fruit smoothie is what percent larger
    14·2 answers
  • What is equivalent to the value of the digit 3 in the number 792.134?
    11·1 answer
  • HELP THIS IS A TEST!!<br> ILL GIVE 20 points!!!
    14·1 answer
  • Henlo can i get a debate on wether the furry fandom deseves all the hate it gets or if it should be more appreciated as a fandom
    15·1 answer
  • Complete the Statement
    7·1 answer
  • The sides of a triangle are represented by 3x-1, 4x+7, and 2x +11. What is th
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!