Question

Complete the following problems using R.

par

492

621

521

561

518

571

538

594

562

629

546

603

532

608

549

601

592

542

601

539

1. A random sample of 20 values of PAR (photosynthetically active radiation) were taken at noon in a certain forest (in moles per meter² per second). Data are included in the assignment .xlsx file. Assume that PAR is approximately normally distributed with a known standard deviation of 40 moles/(m²s).
   1. What is the mean value observed for PAR?
   2. What is the standard error of the mean value of PAR, given this sampling scenario?
2. 3. Find the 95% confidence intervals for the unknown population mean of the PAR values and interpret its meaning.  (Note: for full credit, you must write down a probability statement about the unknown population mean.)
   4. Find the 90% confidence intervals for the unknown population mean of the PAR values and interpret its meaning.
   5. Compare the two intervals.
   6. Test the hypothesis that average PAR value is 550 moles/(m²s), at the =0.05 level.  (Be sure to right down all steps – including hypotheses – as in the lecture notes, and interpret the meaning of the test!)

Answer 1

Solution :

Given that :

a.)

b.)

c.)

95% CI =

We are 95% confident that population mean will fall within the above range.

d.)

90% CI =

We are 90% confident that population mean will fall within the above range.

e.)

95% CI is more wider than 90% CI since, margin of error of 95% CI=17.53 while in 90% CI it is 14.71

f.)

Since P-Value is grater than 0.05 fail to reject H₀ we have enough evidence to conclude that the mean is 550.