Professor Wallace studied over 3,000 elderly individuals for a decade and found a statistically significant relationship between survival rate and number of close friends. Specifically, he found that elderly individuals with few close friends had a much higher death rate. To say that the results of his study are statistically significant means that:

the results are unlikely to have occurred by chance and if the study is repeated under the same condition, a similar result is most likely to be gotten

Explanation:

For a result of a study to be statistically significant means that the result is unlikely to have occurred by chance or error since the error term has been considered during analysis and the study effect was still significant and that the study if repeated under the same conditions will must likely give the same result.