. A city health department wishes to determine if the mean bacteria count per unit volume of

water at a lake beach is below the safety level of 200. Bacteria levels in the lake are typically

normally distributed. A researcher collected 10 water samples of unit volume and found mean

and standard deviation of bacteria counts as 192.7 and 10.8, respectively.

(i) Is this a one-sided or two-sided test, why?

This is a one-sided test, because the interest is in bacteria levels below the safety limit.

(ii) Do the data indicate that there is no cause of concern (assume o=0.05)?

Hypotheses: null & alternative hypotheses:

Ho : # 2 200

HA : / < 200.

Test statistic: since population normal with unknown population variance, use t:

t = -

X - ul

s/ vn

= = to.05.9

Decision rule: n=10 and

0.05,9 =-1.833

reject null hypothesis if tots < -1.833

Observed test statistic: tabs = (192.7 - 200)/(10.8/ v10 ) =-2.14

Because -2.14 < -1.833, the data do not support the null hypothesis so we reject the null

hypothesis and conclude that there is no cause for concern (levels below safety limit)

(iii) Do the data indicate that there is no cause of concern if of=0.01?

At a 1% level of significance, the critical t = 2.821. Since -2.14 > -2.821, we do not have

sufficient evidence to reject the null, so we conclude that there is cause for concern

(levels above safety limit)

(iv) What is the p-value for the test statistic calculated in (ii), and what do you conclude

about the null hypothesis for a=0.05 & 0=0.01?

Can get p-value from online calculator (provided to students in lecture slides):

https://graphpad.com/quickcales/PValue1.cfm