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According to the US Centers for Disease Control, whites born in 1900 had a life expectancy of 47.6 years and nonwhites had a life expectancy of 33.0 years. Assume you survey death records for people born in 1900 in a specific county at random. The average life duration of the 124 whites was 45.3 years, with a standard deviation of 12.7 years. The average life span of the 82 nonwhites was 34.1 years, with a standard deviation of 15.6 years. Conduct a hypothesis test to check if whites and nonwhites in the county have the same average life l

Consider the provided information, sample mean life span of whites $\left({\stackrel{炉}{x}}_1\right)=45.3$years with sample standard deviation $\left(s_1\right)=12.7$years, sample mean life span of non-whites $\left({\stackrel{炉}{x}}_2\right)=34.1$years with sample standard deviation $\left(s_2\right)=15.6$years, sample size of whites $\left(n_1\right)=124$and sample size of non-whites $\left(n_2\right)=82$. The test is two-tailed.

The test statistic and the p-value can be calculated using the TI-83 calculator.

Now to test the difference in the means, follow the steps given below:

Step 1: Press STAT and use the arrow $(鈫�)$to TESTS.

Step 2: Now press the arrow $(鈫�)$to $4:2$-SampTTest and press enter.

Step 3: Then use the arrow $(鈫�)$to STATS and press enter.

Step 4: Now press the arrow $(鈫�)$and enter the inputs as shown below,

Step 5: Then press the arrow $(鈫�)$to calculator and press enter. The output is given below,

From the above output, it can be observed that, the test statistic value is $5.421$and the $蚁$-value is $0.000000234$.