construct a confidence interval estimate of the mean head

1. Construct a confidence interval estimate of the mean head circumference of babies that are 2 months old.  Random sample of 100 babies shows a mean circumference of 40.6cm.  The standard deviation is 1.6cm.  Find a 95 % confidence interval estimate for the mean circumference.  Is there an aspect of the question that is not realistic?

2. A hospital study is completed regarding victims who wore seatbelts.  20 random cases have a symmetric distribution and bell shaped with the mean $9004 and a standard deviation of $5629.  Construct a 99% confidence interval for all costs. 

For Question Numbers 3, 4 and 5:

State the Null Hypothesis and the Alternative Hypothesis.  

Determine the test statistic and P value.

Make a decision regarding the hypothesis based on the P-value and the Level of Significance. 

3. Survey found 75% of restaurant employees stated job stress had a negative impact on personal live.  Sample of 100 employees find 68% answered ‘Yes’ when asked the same question.  Is this a valid reason to think that the proportion of all employees of this chain would say ‘Yes’ differs from the national proportion.  Use a 5% level of significance. 

4.  A sample of 54 bears has a mean weight of 182.9lbs.  The standard deviation is 121.8lbs. Use a 0.05 level of significance to test the claim the population mean of all bear weights is less than 200lbs.

5. Testing the claim that the mean birth weight for all male babies of mothers given vitamins is equal to 3.39kg, which is the mean weight of the population for all male babies, a sample of 16 babies had a mean of 3.675kg and a standard deviation of 0.657. Based on these results, does the vitamin supplement appear to have any effect on the mean birth weight? Use the 0.01 level of significance.