In Norway, the distribution of birth weights for full-term infants whose gestational age is 40 weeks is approximately normal with an unknown mean and...

In Norway, the distribution of birth weights for full-term infants whose gestational age is 40 weeks is approximately normal with an unknown mean and a standard deviation of 430 grams. Suppose that we would like to investigate whether the mean birth weight of full-term babies in this population is lower than 4000 grams.

(1) (2 points) What are the null and alternative hypotheses of the appropriate test?

(2) (6 points)  A random sample of 20 full-term infants is selected from this population. The mean birth weight for this sample is 3900 grams. Using this information, conduct the test in part (1) at the 0.05 level of significance.

      Test statistic:

      P-value:

      Conclusion:

      Interpretation:

(3) (12 points) If the true population mean is as low as 3800 grams and a sample of size 30 is selected from this population, what is the power of the test in part (1) at the 0.05 level of significance?

(4) (4 points) If the true population mean is as low as 3800 grams and the investigator wants to risk only a 10% chance of failing to reject the null hypothesis in part (1), how large a sample size would be required at the 0.05 level of significance?