Question

According to the historical data, the life expectancy in Belgium in less than or equal to the life expectancy in the US. A new study has been made to see whether this has changed. Records of 200 individuals from Belgium who died recently are selected at random. The 200 individuals lived an average of 78.4 years with a standard deviation of 8.2 years. Records of 210 individuals from the US who died recently are selected at random and independently. The 210 individuals lived an average of 76.5 years with a standard deviation of 7.8 years. Assume the population standard deviations of the life expectancies 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, µ₁, in Belgium is greater than the life expectancy µ₂, in the US? Perform a one-tailed test. Then fill in the table below.

Carry out your intermediate computations to at least 3 decimal places and round your answers as specified in the table.

• The Null Hypothesis: H₀ =
• The Alternative Hypothesis: H_{1 =}
• The type of test statistic? Z, t, Chi Square, F
• The value of the test statistic (round to at least 3 decimal places):
• The critical value at the 0.05 level of significance (round to at least 3 decimal places):
• Can we support the claim that the life expectancy in Belgium is greater than the life expectancy in the US? YES or NO

Answer 1