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An obstetrician wants to determine whether a new diet significantly increases
the birth weight of babies. In 2002, birth weight of all full-term babies (gestation
period of 37 to 41 weeks) had a mean of 7.53 pounds. The obstetrician randomly
selects 45 recently pregnant mothers and persuades them to partake of this new
diet. The obstetrician then records the birth weights of the babies and obtains a
sample mean of 7.82 pounds and a sample standard deviation of 1.14 pounds.
a) Is there sufficient evidence to support the claim that the new diet increases the
birth weights of newborns at the α =0.05 level of significance?
Null Hypothesis H0: Population Mean = 7.53 Alternate Hypothesis H1: Population Mean > 7.53 Significance Level α = 5% The name of the TI-83/84 calculator function you will be using: T-Test Are the conditions met in order to use this statistical method? Show how you
YES. We have a random sample and the sample size is large (at least 30), so our Sampling
Distribution for the sample mean should be approximately normal, even if the population we're
sampling from is not normal. From your calculator’s output give the following:
Test Statistic t = 1.71 Interpret what this value is telling you: Our Test Statistic is 1.71 Standard Errors above the hypothesized population mean of
7.53 pounds. P-Value = 4.75% Interpret what this value is telling you: There is a 4.75% probability of getting a Test Statistic this far above (or farther above)
the hypothesized population mean of 753 pounds IF the Null Hypothesis is true. This
probability is small enough to be considered unusual. But we should note that it was
close. Another random sample could have easily been just a little above 5%. So our
results are "marginal".
Which one is your conclusion (Click in the box next to your choice):
Failed to Reject H0
Reject H0 and Accept H1 Page 6 of 9 Show the reason for your conclusion (to prove you weren’t just guessing): P-value < Significance Level
4.75% < 5% So our probability is sma...
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- Winter '08
- Statistics, Statistical hypothesis testing, significance level