The study examines the average life expectancy of G20 countries using a one-sample hypothesis test. The sample consists of 10 randomly generated G20 countries with a mean of 75.4 years with a standard deviation of 4.675 years. After the resulting computation of the test statistic, t = 2.097 will be used to decide whether the null hypothesis will be rejected or will fail to be rejected. Following the decision rule, if the test statistic falls within the critical region (z > 1.645), we will reject the null hypothesis (H0: µ ≤ 78.6 (mean life expectancy is below the test value)). Thus, (t = 2.097) > 1.645 which means that we reject the null hypothesis (H0). This implies that we accept the alternate hypothesis (H1: µ > 78.6 (mean life expectancy is greater than the test value)). This means that the probability that the average life expectancy of G20 nations is greater than 78.6 years has a 95 percent level of confidence. In conclusion, there is sufficient evidence that the average life expectancy of people living in G20 countries is greater than 78.6 years.
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The findings in this hypothesis testing will help in the decision making about the probable value of the average life expectancy of people in the G20 countries using only a sample of 10 random G20 countries. The research question that we want to answer is what the average life expectancy among the G20 nations is. The hypothesis testing is a method in which the probable value of the parameter of a population is decided from a specific set of sample. Hypothesis testing is a very important step in the determination of possible value of a parameter of a given population. In this case, the parameter (average life expectancy) of a population (G20 countries) is studied using a sample (10 randomly generated G20 countries).