Statistical Hypothesis Testing

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1.  (12 points)  In this recession, yours truly would like to make extra money to support his frequent filet-mignon-et-double-lobster-tail dinner habit.  A promising enterprise is to mass-produce garnet wedding rings for brides.  Based on my diligent research, I have found out that women's ring size normally distributed with a mean of 6.0, and a standard deviation of 1.0.  I am going to order 5000 garnet wedding rings from my reliable Siberian source.  They will manufacture ring size from 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, and 9.5.  How many wedding rings should I order for each of the ring size if I order 5000 rings altogether?  (Note: It is natural  to assume that if your ring size falls between two of the above standard manufacturing size, you will take the bigger of the two.)

2.  (8 points)  According to a study by my PseudoScientific Consulting, the time interval between Atlantic hurricane of category 4 has a mean of 456 days and a standard deviation of 123 days.  Suppose that you observe a sample of five (5) time intervals between successive category 4 hurricanes.         a.  On average, what would you expect to be the mean of the five (5) time intervals?         b.  How much variation would you expect from your answer in part (a)?    (Hint: Think along the line of the Empirical 68-95-99.7 Rule.)  

The following information is for Questions 3 through 8.
    The recommended daily allowance (RDA) of cobalamine (Vitamin B12) for growing teens is 2.4 µg (micrograms).  My brother takes it upon himself to make sure that everyone gets the recommended daily allowance.  It is generally believed that growing teens are getting less than the RDA of 2.4 µg of cobalamine daily.     It is an open secret that my brother's Au & Associates FauxPharmaceutical (AFP) peddles dietary supplements around the globe.  It is claimed by representatives of AFP that by taking their vitamin supplement extracted from Atlantic scrod, brand-named as...
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