Assume the average weight of a full-term newborn infant (i.e. 39-40 weeks gestat

Question

Assume the average weight of a full-term newborn infant (i.e. 39-40 weeks gestation) in the US is 3400g. Suppose we measure the birth weight of 1000 (full-term) infants born to alcoholic mothers. We find that the sample mean birth weight is 3200g, and the sample standard deviation is 500g.

a. Calculate a 95% confidence interval for the population mean birth weight of infants born to alcoholic mothers.

1.96*500sqrt(1000)= 30, 3200+/- 98= (3102,3298) <---- Is this right?

b. Suppose we want to test the hypothesis

H0: ? = 3400g

H1: ? ? 3400g

where ? is the population mean birth weight for offspring of alcoholic mothers. Using the confidence interval you calculated in (a), would you reject or fail to reject H0 at ? = 0.05? (Recall the close relationship between confidence intervals and hypothesis testing. Suppose you want to test a hypothesis H0: ? = ?o versus H1: ? ? ?o using ? = .05. You can test this hypothesis using a confidence interval with this rule: If ?o is OUTSIDE the 95% CI then REJECT the null hypothesis; if ?o is INSIDE the 95% CI then DO NOT REJECT the null hypothesis.)

The null would be rejected, correct?

c. Compute the following test statistic for the two-sided hypothesis test in part (b):

Is the p-value based on this test statistic less than 0.05?

I'm not sure how to go about doing this one...

Explanation / Answer

a)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    3200          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    500          
n = sample size =    1000          
              
Thus,              
Margin of Error E =    30.98975162          
Lower bound =    3169.010248          
Upper bound =    3230.989752          
              
Thus, the confidence interval is              
              
(   3169.010248   ,   3230.989752   ) [ANSWER]

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