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 20 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 32 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, 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:=36μ H1:≠36μ (b) Determine the type of test statistic to use. ▼t Degrees of freedom: (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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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Question

The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is

centimeters. To check whether this is still accurate, heights are measured for a random sample of

Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are

centimeters and

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,

, 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:=36μ
H1:≠36μ
(b)	Determine the type of test statistic to use.
	▼t	Degrees of freedom:
(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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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