The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 40 centimeters. To check whether this is still accurate, heights are measured for a random sample of 13 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 48 centimeters and 11 centimeters, respectively. Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated begonias,
μ , is different from that reported in the journal? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis
H0
and the alternative hypothesis
H1.
H0:
H1:
(b) Determine the type of test statistic to use.
▼(Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the p-value. (Round to three or more decimal places.)
(e) Can it be concluded that the mean height of treated Begonias is different from that reported in the journal?
Yes
No