It is claimed that the average weight of babies at birth is 3.4 kg. The average weight of a random sample of 30 newly born babies was determined. It was found out that the average weight was 3.1 kg. Is there a reason to believe that the average weight of babies at birth is not 3.4 kg? Assume that the population standard deviation is 1.1 kg. Use 0.05 level of significance.
Null and alternative hypotheses:
Because σ is known and we can use the z-test.
The standardized test statistic is
In z-table the area corresponding to is 0.0681. Because the test is a two-tailed test, the P-value is equal to twice the area to the left of ,
Because the P-value is greater than α = 0.05, we fail to reject the null hypothesis, there is not enough evidence at the 5% level of significance to support the claim that the average weight of babies at birth is not 3.4 kg.
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