A certain drug is claimed by its manufacturers to reduce overweight men by 4.75 kg per month,
with a standard deviation of 0.89 kg. Ten randomly chosen men reported losing an average of 4.25 kg
within a month. Does this data support the claim of the manufacturer at 0.05 level of significance?
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is and the critical value for a two-tailed test is
The rejection region for this two-tailed test is
The z-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population is different than at the significance level.
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