The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 19 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 39 centimeters and 10 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, u, 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 H and the alternative hypothesis H₁. : H₁:0 (b) Determine the type of test statistic to use. (Choose one) F |x X D S OSO p

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient
is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 19 Begonias
grown while being treated with the nutrient. The sample mean and sample standard deviation of those height
measurements are 39 centimeters and 10 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, u, 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 H and the alternative hypothesis H₁.
H₁0
(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?
OYes O No
μ
X
D
S
06
0=0 ☐☐
p
Â
olo
☐☐
☐☐ □口 O>0
Transcribed Image Text:The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 19 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 39 centimeters and 10 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, u, 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 H and the alternative hypothesis H₁. H₁0 (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? OYes O No μ X D S 06 0=0 ☐☐ p  olo ☐☐ ☐☐ □口 O>0
Expert Solution
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given data n=19x¯=39s=10claim μ36two-tailed test 

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