Question

1. Data was collected measuring the overall mass of the spiny-backed bacteria (ug) found growing on rock faces around SHSU campus. If the mass of this random sample collected across campus is significantly different than zero, there is concern that a spiny-backed bacteria outbreak will occur soon.  Help out the University and run the proper t-test on this bacteria mass data:

0.25 1.63 2.22 2.46 2.42 2.45 1.64 2.10 1.69 2.34 1.34 2.34 0.99 3.03 4.16 0.00 3.12

3.04 2.40 1.49

1. First, state your null and alternative hypotheses in the proper format
2. Have a look at your data; is it normally distributed?
3. Which type of t-test and why and calculate the t-statistic (by hand, show your work)
4. Now in R – code & results
5. What can you conclude based on your analyses?

Answer 1

(d) The R code and the results are given below:

> x=c(0.25, 1.63, 2.22, 2.46, 2.42, 2.45, 1.64, 2.10, 1.69, 2.34, 1.34, 2.34, 0.99, 3.03, 4.16, 0.00, 3.12, 3.04, 2.40, 1.49)
> t.test(x,mu=0,)

One Sample t-test

data: x
t = 9.397, df = 19, p-value = 1.419e-08
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
1.597672 2.513328
sample estimates:
mean of x
2.0555

(e) From the R code result above, we conclude that since p-value is less than 0.05, we reject the null hypothesis. We further conclude that there is enough evidence to suggest that the mass of the spiny-backed bacteria is significantly different than zero.