Chisonga randomly samples 60 people, and finds that 18 respondents report high mental distress, while the other 42 report low mental distress. He wants to know if respondents with high mental distress differ in how much they worry compared to those with low mental distress. To test this, he counts the number of worrying thoughts reported by individuals in both groups. Descriptive statistics for those with low and high mental distress are shown in the table below.

LOW MENTAL DISTRESS:

average # worrying thoughts: 33

standard deviation of worrying thoughts: 10.3

n: 42

HIGH MENTAL DISTRESS:

average # worrying thoughts: 49

standard deviation of worrying thoughts: 22.1

n: 18

Perform a hypothesis test to determine whether respondent with low and high levels of mental distress differ in the number of worrying thoughts they have (use an alpha level of 0.05).

What is the value of the test statistic from the hypothesis test?

What is the critical test value for the test?

What conclusion can you draw based on the data?