Question

You wonder if one's age is independent of whether or not one's willingness to wear masks in public. You ask 100 people whether they are wearing masks in public or not and whether they are under 20 years old, between 20 and 39, between 40 and 59, or 60 or above. Using your data, you calculate a test statistic of 16.5. Using a critical value of 7.82, what is your statistical conclusion?

a) Your results are significant; one's willingness to wear masks is not independent of one's age. b)Your results are significant; one's willingness to wear masks is independent of one's age.
c)Your results are not significant; one's willingness to wear masks is independent of one's age.
d) Your results are not significant; one's willingness to wear masks is not independent of one's age.​

Answer 1

The statistical conclusion is:

a) Your results are significant; one's willingness to wear masks is not independent of one's age.

Explanation:

From this experiment,

The null hypothesis is established as:

H 0 = one's willingness to wear masks is independent of one's age.

The alternate hypothesis is established as:

H 1 = one's willingness to wear masks is not independent of one's age.

In statistics, if the absolute value of the test statistic is greater than the critical value, we declare statistical significance and reject the null hypothesis.

Since the test statistic = 16.5, which is higher than the critical value of 7.82, this establishes statistical significance. Thus, the null hypothesis is rejected.

Therefore, the statistical conclusion is that one's willingness to wear masks is not independent of one's age.