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# Hypothesis Test: Two-tailed Test of Difference Between Means

According to the historical data, the life expectancy in Argentina is equal to the life expectancy in Bolivia. A new study has been made to see whether this has changed. Records of 295 individuals from Argentina who died recently are selected at random. The 295 individuals lived an average of 74.8 years with a standard deviation of 4.6 years. Records of 290 individuals from Bolivia who died recently are selected at random and independently. The 290 individuals lived an average of 75.4 years with a standard deviation of 4.4 years. Assume that the population standard deviation of the life expectancy can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the life expectancy, u1, in Argentina is not equal to the life expectancy, u2, in Bolivia anymore? Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

null hypothesis:
alternative hypothesis:
type of test statistic:

value of the test statistic rounded to at least 3 decimal places:
the two critical values at the 0.05 level of significance rounded to at least 3 decimal places:
can we support the claim that the life expectancy in Argentina is not equal to the life expectancy in Bolivia? yes or no

#### Solution Preview

null hypothesis:
Null Hypothesis: Ho: M 1=M 2 There is no difference between the mean life expectancy in Argentina and Bolivia
alternative hypothesis:
Alternative Hypothesis: H1: M 1not equal to M 2 There is difference between the mean life expectancy in Argentina and Bolivia

type of test statistic: z-value

value of the test statistic rounded to at least 3 decimal places:

value of the test statistic rounded to at least 3 decimal places:

Argentina; Bolivia
Mean =M = 74.80 75.40 ...

#### Solution Summary

The solution tests the hypothesis that the life expectancy, u1, in Argentina is not equal to the life expectancy, u2, in Bolivia.

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