Question: One scientific test of whiteness study mentioned in Example 1

One scientific “test of whiteness” study mentioned in Example 1 tested the effect of a self applied tooth-whitening peroxide gel system in a randomized, controlled clinical trial. 11 The 58 adults assigned to the gel whitening group applied the gel after normal brushing according to the manufacturer’s instructions. The fluoride toothpaste group was instructed to brush twice a day. The procedure was repeated for both groups twice a day for 14 days. An experienced examiner determined the tooth shades comparing each tooth to the shade tabs from an accepted shade scale (Vita shade guide) at the start of the experiment to create a baseline and then after one and two weeks of product application. Changes between the baseline score and the one- and two-week assessments were expressed as a difference of the respective Vita score, with a positive difference indicating an improvement in tooth whiteness. The results of the study are shown in the table in the next column.
Mean Vita Shade Score Recorded at Two Weeks and Change
a. State the hypotheses that were tested for the change from baseline means.
b. The P-value is reported as 6 0.05 for the test comparing the means. Explain how to interpret this value.
c. Calculate the pooled standard error, the t statistic, and the resulting P-value.
d. The ratio of the change from baseline sample means was 2.91. Interpret this ratio.

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