Question

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 26.9 and the standard deviation of the Flesch scores was 14.1. For a representative sample of pages from WebMD, the mean score was 43.3 and the standard deviation was 19.2. Suppose that these means and standard deviations were based on samples of 40 pages from each site. Is there convincing evidence that the mean reading level for health-related pages differs for Wikipedia and WebMD? Test the relevant hypotheses using a significance level of α = 0.05. (Use μ1 for Wikipedia and μ2 for WebMD.)

State the appropriate null and alternative hypotheses.

H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0

H0: μ1 − μ2 ≠ 0 Ha: μ1 − μ2 = 0

H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0

H0: μ1 − μ2 = 0 Ha: μ1 − μ2 > 0

H0: μ1 − μ2 < 0 Ha: μ1 − μ2 = 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

t =

P-value =

State the conclusion in the problem context.

We fail to reject H0. There is convincing evidence that the mean reading level for health-related pages differs for Wikipedia and WebMD.

We fail to reject H0. There is not convincing evidence that the mean reading level for health-related pages differs for Wikipedia and WebMD.

We reject H0. There is not convincing evidence that the mean reading level for health-related pages differs for Wikipedia and WebMD.

We reject H0. There is convincing evidence that the mean reading level for health-related pages differs for Wikipedia and WebMD.

Answer 1

Given that,

For Wikipedia :

For WebMD :

The null and the alternative hypotheses are,

H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 ≠ 0

Using TI-84 calculator we get,

Test statistic is t = -4.4

P-value = 0.000

Since, p-value = 0.000 < α = 0.05

We reject H0. There is convincing evidence that the mean reading level for health-related pages differs for Wikipedia and WebMD.