Question

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.

State the null and alternative hypotheses.

a. $H_0:$

b. $H_a$ :

Short answer

(a) The required hypotheses$H_0:{\mu }_{\text{whites}}={\mu }_{\text{nonwhites}}$

(b) The required hypotheses$H_1:{\mu }_{\text{whites}}\ne {\mu }_{\text{nonwhites}}$

Step-by-step solution

Part (a) Step 1: Given information 

According to the US Centers for Disease Control, the average life expectancy for whites born in 1900 was $47. years and 33 years for nonwhites. 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 duration 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 lengths.

Part (a) Step 2: State the null and alternative hypotheses.

The null hypothesis is given below,

$H_0:{\mu }_{\text{whites}}={\mu }_{\text{nonwhites}}$

Part (b) Step 1: Given information 

According to the US Centers for Disease Control, the average life expectancy for whites born in 1900 was $47. years and 33 years for nonwhites. 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 duration 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 lengths.

Part (b) Step 2: State the null and alternative hypotheses.

The alternative hypothesis is given below,

$H_1:{\mu }_{\text{whites}}\ne {\mu }_{\text{nonwhites}}$