Question

A simple random sample was taken of 44 water bottles from a bottling plant's warehouse. The dissolved oxygen content (in mg/L) was measured for each bottle, with the results below:

1.53, 8.35, 11.66, 11.54, 9.83, 5.92, 7.14, 8.41, 8.99, 13.81, 10.53, 7.4, 6.7, 8.42, 8.4, 8.18, 9.5, 7.22, 9.87,
6.52, 8.55, 9.75, 9.27, 10.61, 8.89, 10.01, 11.17, 7.62, 6.43, 9.09, 8.53, 7.91, 8.13, 7.7, 10.45, 11.3, 10.98, 8.14,
11.48, 8.44, 12.52, 10.12, 8.09, 7.34

a. Create a histogram and QQ plot of the data using R. Is it plausible that the data was drawn from a population that follows a normal distribution? Explain your answer.
b. Find a 98% condence interval for the population mean dissolved oxygen content.
c. Interpret the interval you created in (b)
Show all codes used in R.

Answer 1

Answer:

a. Yes. p-value(0.05469)> 0.05

b,c- see details below

Step-by-step explanation:

a.  #Use shapiro test to test for normality

Yes. The population has a p-value greater than 0.05:

0.05469>0.05

b.From our output, the 98% intervals are:

[8.19016,9.648021]

c. The new interval, [8.19016,9.648021] is wider, but we are more confident that it contains the true mean ( 8.919091)

#Attached histogram and snippet of the applicable code.