The makers of the Oral-B 3D toothbrush claims that using their brush will "significantly combat tooth decay" when compared with regular toothbrushes. College students have an average of 0.70 (s = 0.40) cavities filled in a given year. You randomly ask 100 students to use the Oral-B 3D toothbrush for one year. They have an average of 0.631 cavities filled in that year.  Does the Oral-B 3D toothbrush combat tooth decay at a significance level of .05?  Complete a hypothesis test of this study that the using the Oral-B 3D toothbrush reduces (e.g., a "directional" hypothesis) tooth decay.  Be sure to include all six steps of a hypothesis test.

Submit a document with the answers to the following questions along with an Excel workbook with the appropriate computations. Be sure to report the appropriate statistics.

1. The makers of the Oral-B 3D toothbrush claims that using their brush will "significantly combat tooth decay" when compared with regular toothbrushes. College students have an average of 0.70 (s = 0.40) cavities filled in a given year. You randomly ask 100 students to use the Oral-B 3D toothbrush for one year. They have an average of 0.631 cavities filled in that year.  Does the Oral-B 3D toothbrush combat tooth decay at a significance level of .05?  Complete a hypothesis test of this study that the using the Oral-B 3D toothbrush reduces (e.g., a "directional" hypothesis) tooth decay.  Be sure to include all six steps of a hypothesis test.

    2. Your best friend would like to attend dental school, and wants to study the effects of using the Oral-B 3D toothbrush. They randomly select 21 college students and asks them to use the toothbrush for 1 year.  After that year, those 21 students have the following number of cavities:

            0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 4, 0, 1

Your friend claims to have more significant results than you because their group had, on average, fewer cavities.  You claim that their results were not significant at the .05 level, even though their study had fewer cavities, on average.  Complete a 6-step hypothesis test, using your friend's results, that the Oral-B 3D toothbrush combats tooth decay at the .05 level of significance. 

    3. You suspect that a new birth control pill affects blood pressure given its chemical makeup.You randomly select 10 women and give them the new birth control pill for a month. The diastolic blood pressure of the ten women on the birth control pill are presented below:

68, 76, 69, 78, 74, 85, 79, 78, 80, 81

Does the new birth control pill affect blood pressure (m = 75)?  Complete a 6-step hypothesis test with alpha = .05.

    4. A medical researcher is convinced that you’re wrong and completes their own study with 15 women. They give the same drug for the same amount of time and measure blood pressure, obtaining the following data:

            75, 75, 78, 76, 78, 78, 74, 72, 80, 82, 76, 77, 76, 77, 78

Complete a 6-step hypothesis test with alpha = .05. What would this medical researcher conclude? How is this study different from yours? Why are the conclusions different? How is it that you have EXACTLY the same mean, but come to different conclusions?

    5. A researcher knows that the mean number of symptoms (e.g., fatigue, sleep disturbance, feelings of worthlessness, etc.) exhibited by the population of people with unipolar depression, prior to diagnosis, is 9.5. They suspect that being told that you suffer from unipolar depression increases that number. They randomly select 14 individuals already with the diagnosis of unipolar depression and counts the number of symptoms they exhibit. The number of depressive symptoms exhibited by the 14 participants was:

            8, 9, 15, 19, 12, 8, 16, 14, 12, 13, 16, 5, 19, 10 

Does the researcher’s hypothesis carry any weight at the .05 level? Complete a 6-step hypothesis test with alpha