Question

4. Flu cases this past flu season (4 months or 20 weeks) in the Butterfield, Kansas, school system were about 15 per week. For the entire state, the weekly average was 16 and the standard deviation 2.35. Are the kids in Butterfield as sick as the kids throughout the state? Do this one manually.
what is the calulation

Answer 1

Answer: Yes, the kids in the Butterfield are as sick as the kids throughout the state.

Explanation:

Since we have given that

$\mu=16\\\sigma=2.35$

Let our hypothesis be

$H_0:\mu=16\\H_1:\mu\neq 16$

As we know the formula,

$z=\frac{X-\mu}{\frac{\sigma}{\sqrt n}}\\\\z=\frac{15-16}{\frac{2.35}{\sqrt {20}}}\\\\z=\frac{-1}{0.525}=(-)1.904$

At 5% level of significance ,

$critical\ z=\pm 1.96$

Since,

$-1.904>-1.96$

Hence, we accepted the hypothesis i.e.

$H_0:\mu=16$

Hence,

Yes, the kids in the Butterfield are as sick as the kids throughout the state.

Answer 2

ANSWER IS ATTACHED BELOW