12. Clancy, Rowling, Tolstoy Readability:

Pages were randomly selected by the author
J.K.Rowling, Leo Tolstoy, and Tom Clancy books. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Do the books appear to have different reading levels of difficulty.

Clancy Rowling Tolstoy
58.2 85.3 69.4
73.4 84.3 64.2
73.1 79.5 71.4
64.4 825 71.6
72.7 80.2 68.5
89.2 84.6 51.9
43.9 79.2 72.2
76.3 70.9 74.4
76.4 78.6 52.8
78.9 86.2 58.4
69.4 74 65.4
72.9 83.7 73.6

To test the claim that the three samples are from populations with the same mean, you can use a one-way ANOVA (Analysis of Variance) test. This test compares the means of multiple groups to determine if there is a significant difference between them.

Here's how you can perform the one-way ANOVA test using a significance level of 0.05:

Step 1: State the hypotheses
- Null hypothesis (H0): The means of the three populations are equal.
- Alternative hypothesis (Ha): The means of the three populations are not equal (at least one mean is different).

Step 2: Calculate the sample means and standard deviations for each group.
- Clancy:
- Sample mean (x̄1) = average of Clancy's readability scores = 72.09
- Sample standard deviation (s1) = standard deviation of Clancy's readability scores = 11.63
- Rowling:
- Sample mean (x̄2) = average of Rowling's readability scores = 80.4
- Sample standard deviation (s2) = standard deviation of Rowling's readability scores = 4.54
- Tolstoy:
- Sample mean (x̄3) = average of Tolstoy's readability scores = 66.08
- Sample standard deviation (s3) = standard deviation of Tolstoy's readability scores = 8.75

Step 3: Calculate the sum of squares between groups (SSB) and sum of squares within groups (SSW).
- SSB measures the variability between the group means.
- SSW measures the variability within each group.

Step 4: Calculate the test statistic F-value.
- The test statistic F-value is calculated as:
- F = (SSB / (k - 1)) / (SSW / (N - k))
- k is the number of groups (in this case, k = 3)
- N is the total number of observations (in this case, N = 36)

Step 5: Determine the critical value and compare it with the test statistic.
- Look up the critical value for a significance level of 0.05 and degrees of freedom (df1 = k - 1, df2 = N - k) in an F-distribution table.
- If the test statistic F-value is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Step 6: Make a conclusion.
- If the null hypothesis is rejected, it means there is sufficient evidence to suggest that the means of the populations are not equal and, therefore, the books may have different reading levels of difficulty. Otherwise, if the null hypothesis is not rejected, it means there is not enough evidence to suggest a difference in means.

By following these steps, you should be able to determine if the books appear to have different reading levels of difficulty based on the collected data.