Solution to 1.It is claimed that the average weight of babies at birth is 3.4 kg. The … - Sikademy
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Peace Awoke

1.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 1.1kg. Use 0.05 level of significance.

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The following null and alternative hypotheses need to be tested:



This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

Based on the information provided, the significance level is \alpha = 0.05, df=n-1=29 degrees of freedom, and the critical value for a two-tailed test is t_c = 2.04523.

The rejection region for this two-tailed test is R = \{t: |t| > 2.04523\}.

The t-statistic is computed as follows:


Since it is observed that |t| = 1.49379\le 2.04523=t_c, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value for two-tailed, df=29 degrees of freedom, t=-1.49379, is p=0.146032, and since p=0.146032>0.05=\alpha, it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean \mu is different than 3.4, at the \alpha = 0.05 significance level.

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