Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

Calculate the test statistic and p-value.

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 $\left({\overline{x}}_1\right)=45.3$years with sample standard deviation $\left(s_1\right)=12.7$years, sample mean life span of non-whites $\left({\overline{x}}_2\right)=34.1$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 $(\to )$to TESTS.

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

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

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

Step 5: Then press the arrow $(\downarrow )$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 $\rho$-value is $0.000000234$.