Problem 8.

Suppose an investigator takes a random sample of n = 50 birth weights from several teaching hospitals located in an inner-city neighborhood. In her random sample, the sample mean x is 3,150 grams and the standard deviation is 250 grams. (2 pts)

1. Calculate a 95% confidence interval for the population mean birth weight in these hospitals.(1 pt)
2. The typical weight of a baby at birth for the US population is 3,250 grams. The investigator suspects that the birth weights of babies in these teaching hospitals is different than 3,250 grams, but she is not sure if it is smaller (from malnutrition) or larger (because of obesity prevalence in mothers giving birth at these hospitals). Carry out the hypothesis test that she would conduct. (1 pt)

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Problem 9. Testing for fibromyalgia.

A patient named Diana was diagnosed with fibromyalgia, a long-term syndrome of body pain, and was prescribed anti-depressants. Being the skeptic that she is, Diana didn't initially believe that anti-depressants would help her symptoms. However after a couple months of being on the medication she decides that the anti-depressants are working, because she feels like her symptoms are in fact getting better. (1.5 pts)

1. Write the hypotheses in words for Diana's skeptical position when she started taking the anti-depressants. (0.5 pts)
2. What is a Type 1 Error in this context? (0.5 pts)
3. What is a Type 2 Error in this context? (0.5 pts)