Suppose the healthy mean birth weight of new born babies is

Suppose the healthy mean birth weight of new born babies is 71bs. To see if babies born to mothers who worked until they delivered their baby have lower birth weight on average, a sample of 28 pregnant working women were enrolled in the study, and the birth weight of their baby recorded. The mean birth weight was 6.8 lbs, with a standard deviation of 1.5 lbs. Conduct a hypothesis test to answer this question at the 5% significance level.

Solution

Set Up Hypothesis
Null, Average birth weight is same H0: U>7
Alternate, birth weight is lower H1: U<7
Test Statistic
Population Mean(U)=7
Sample X(Mean)=6.8
Standard Deviation(S.D)=1.5
Number (n)=28
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =6.8-7/(1.5/Sqrt(27))
to =-0.706
| to | =0.706
Critical Value
The Value of |t | with n-1 = 27 d.f is 1.703
We got |to| =0.706 & | t | =1.703
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -0.7055 ) = 0.24326
Hence Value of P0.05 < 0.24326,Here We Do not Reject Ho

We don\'t have enough evidence to support the birth
weight lower than 7