Question

Another team of researchers wants to examine if the social interactions of Indian senior citizens who live in the United States differs by the ethnic composition of the community they live in. So, they collect two random samples of Indian American adults aged 70+. One sample comprises 43 Indian American seniors living in a typical retirement community in Florida with a largely white population. The other sample comprises 37 Indian American seniors living in Shanti Niketan, a retirement community for Indian Americans known as “Little India,” which is also located in Florida. The researchers collect the number of face‐to face interactions that each senior has with their neighbors on a daily basis. The sample of 43 seniors living in the typical retirement community had a mean of 1.42 daily interactions with a standard deviation of 0.10. The sample of 37 seniors living in Shanti Niketan had a mean of 1.58 daily interactions with a standard deviation of 0.78. Does Indian American seniors mean amount of neighbor interaction differ between the two retirement communities?

a. State hypotheses in notation and sentences.

b. Calculate the t test statistic.

c. Find the critical t* value using an alpha (α) of 0.01.

d. State your conclusion in reference to the null hypothesis (α=.01).

e. Interpret your result in reference to the alternative hypothesis.