Question

A sample of the birth weight for 25 newborn male babies was taken from babies whose mother took prenatal vitamin supplements. The results of the study showed an average birth weight of 3.953 kg and a standard deviation of 0.552 kg. The claim is that taking vitamin supplements increase the baby’s birth weight. The mean birth weight for all male babies is 3.58 kg

1. What can you conclude by comparing the 95% Confidence Interval and the mean weigh of all male babies (3.58 kg)? Justify your answer.

2. In performing a formal Test of Hypothesis to determine if the taking of prenatal vitamins will increase the birth weight of babies (using the above summary data), the formal hypothesis for this test would be:

3. Using the infant birth weight information from above, find the appropriate critical student t-value (t-critical) for performing the test of hypothesis.

4. Perform the 1-sample t-test to obtain the t-calc for the test of hypothesis.

5. In comparing t-critical and t-calc, state your conclusion for this test of hypothesis. Justify your answer.

Answer 1

1)

sample mean, xbar = 3.953
sample standard deviation, s = 0.552
sample size, n = 25
degrees of freedom, df = n - 1 = 24

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.064

ME = tc * s/sqrt(n)
ME = 2.064 * 0.552/sqrt(25)
ME = 0.228

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (3.953 - 2.064 * 0.552/sqrt(25) , 3.953 + 2.064 * 0.552/sqrt(25))
CI = (3.73 , 4.18)

as the confidenc einterval does not contian 3.58 reject H0

2)

One sample t test

3)

This is right tailed test, for α = 0.05 and df = 24
Critical value of t is 1.711.
Hence reject H0 if t > 1.711

4)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (3.953 - 3.58)/(0.552/sqrt(25))
t = 3.379

5)

AS test tsatistic > 1.711 Reject H0