A study was done to see if there is a difference between the number of sick days people without children take and the number of sick days people with children take. A random sample of 9 childless people found that the mean of the number of sick days taken was 5.5. The standard deviation of the sample was 1.23. A random sample of 7 people with at least one child found that the mean was 4.3 days and a standard deviation of 1.19 days. At \(\alpha=0.05\), can it be concluded that there is a difference in the means?

Step 1: 

Identify the hypothesis and claim

\[H_0:\mu_1-\mu_2=0\;\;\;\;\;\;\; H_1:\mu_1- \mu_2\neq0\text{ (Claim)}\]

Step 2:

Collect the data

\[n_1=9\]

\[n_2=7\]

\[\overline{x}_1=5.5\]

\[\overline{x}_2=4.3\]

\[s_1=1.23\]

\[s_2=1.19\]

\[\alpha=0.05\]

Step 3: 

Plug into the hypothesis Calculator!

Now you can use any method and you have all of the needed data. Let's do my favorite P-Value

Step 4: 

Analysis and conclusion.

Note that \(p>1-\frac{\alpha}{2}\) i.e.

\[0.975679>0.975\]

hence we reject \(H_0\) and there is enough evidence to support the claim.