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

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!!!