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# Hypothesis Testing and Confidence Intervals for Means

1) We wish to estimate the mean serum indirect bilirubin level of 4-day-old infants. The mean for a sample of 160 infants was found to be 5.98 mg/100 cc. Assume that bilirubin levels in 4-day-old infants are approximately normally distributed with a standard deviation of 3.5 mg/100 cc. Construct a 95% confidence interval for the true mean bilirubin level in 4-day-old infants.

2) A researcher studied the effects of pancuronium-induced muscle relaxation on circulating plasma volume on newborn infants weighing more than 1700 grams who required respiratory assistance within the first 24 hours of birth and met other clinical criteria. The following table is a result of measurements of plasma volume (ml) made during mechanical ventilation.

Subject group Sample size Sample mean Sample st. dev.
paralyzed 5 48.0 8.1
nonparalyzed 7 56.7 8.1

a. You may assume equal standard deviations. Construct a 98% confidence interval for the difference of the two population means.
b. What are your conclusions? Do you think there is a difference between the two population means?

3) A local weight-loss company suggests that the average client loses 15 pounds during the first month. A consumer advocate group feels that the actual number of pounds lost is much less than this. To test the claim, they select 30 of the clients at random and obtain the following data: Pounds Lost During the 1st Month: 16 20 14 15 14 18 19 20 9 13 20 11 12 18 13 17 11 21 14 15 15 13 17 12 9 20 16 18 21 11
A hypothesis test is conducted.
a. State the null and alternative hypotheses.
b. The test statistic is t = 0.6107 with p-value = 0.7269. Based on this information, what is the conclusion of the hypothesis test? Justify your answer.

4) The following data presents tests scores on a Behavioral Vignettes Test for self-help skill teaching for the primary parents of a random sample of families with mentally retarded children before and after a training program.
Before 7 6 10 16 8 13 8 14
After 11 14 16 17 9 15 9 17
Based on this information, can you conclude that the training program is effective? Use a significance level of 0.05. State your assumptions.