Hypothesis test for the difference of population means: Z test

According to the historical data, the life expectancy in the United States is equal to the life expectancy in Japan. A new study has been made to see whether this has changed. Records of 300 individuals from the United States who died recently are selected at random. The 300 individuals lived an average of 77.5 years with a standard deviation of 4.4 years. Records of 270 individuals from Japan who died recently are selected at random and independently. The 270 individuals lived an average of 76.7 years with a standard deviation of 5.0 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 0.1 level of significance, is there enough evidence to support the claim that the life expectancy, u, in the United States is not equal to the life expectancy, u,, in Japan 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. (If necessary, consult a list of formulas.) The null hypothesis: H :I P X S P The alternative hypothesis: H : 1 The type of test statistic: (Choose one) 0=0 090 020 0*0 00 The value of the test statistic: (Round to at least three decimal places.) 0 X 5 ? The two critical values at the 0. 1 level of significance: Round to at least three [ and ]] decimal places.) Can we support the claim that the life expectancy in the United States is not equal to the life expectancy O Yes O No in Japan