An adventure company runs two obstacle courses, Fundash and Coolsprint, with similar designs. Since Fundash was built on rougher terrain, the designer of the courses suspects that the mean completion time of Fundash is greater than the mean completion time of Coolsprint. To test this, she selects 230 Fundash runners and 275 Coolsprint runners. (Consider these as independent random samples of the Fundash and Coolspring runners.) The 230 Fundash runners complete the course with a mean time of 78.5 minutes and a standard deviation of 8.1 minutes. The 275 individuals complete Coolsprint with a mean time of 76.7 minutes and a standard deviation of 6.5 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.01 level of significance, is there enough evidence to support the claim that the mean completion time, ₁, of Fundash is greater than the mean completion time, H₂ of Coolsprint? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho H₁ :0 (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 we support the claim that the mean completion time of Fundash is greater than the mean completion time of Coolsprint? OYes No μ X 4 a S X 2 On ロ=ロ OSO ☐☐ OO

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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SLICE NAME Confidence Intervals and Hypothesis Testing TOPIC NAME Hypothesis test for the difference of population means: Z test

Done
O CONFIDENCE INTERVALS AND HYPOTHESIS...
Hypothesis test for the difference... O▬▬0
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(a) State the null hypothesis Ho and the alternative hypothesis H₁.
HO
H₁:0
(b Determine the pe of test statistic to use.
(Choose one) ▼
(c) Fit
Español
An adventure company runs two obstacle courses, Fundash and Co
with similar designs. Since Fundash was built on rougher terrain, th
designer of the courses suspects that the mean completion time of
is greater than the mean completion time of Coolsprint. To test this
selects 230 Fundash runners and 275 Coolsprint runners. (Consider th
independent random samples of the Fundash and Coolspring runne
230 Fundash runners complete the course with a mean time of 75 m
and a standard deviation of 8.1 minutes. The 275 individuals complete
Coolsprint with a mean time of 76.7 minutes and a standard deviatio
minutes. Assume that the population standard deviations of the com
times can be estimated to be the sample standard deviations, since
samples that are used to compute them are quite large. At the 0.01
significance, is there enough evidence to support the claim that the
completion time, ₁, of Fundash is greater than the mean completio
12 of Coolsprint? Perform a one-tailed test. Then complete the part
Chi-Square
Carry your intermediate computations to at least three decimal pla
necessary, consult a list of formulas.)
F
(d) and the p-value Round to three or more decimal places.)
☐
Explanation
0/5
0/5
tes statistic. (Round to three or more decimal places.)
(e) Can we support the claim that the mean completion time of Fundash is
greater than the mean completion time of Coolsprint?
OYes No
Check
AA
Evelyn V
μ
X
89
ローロ
O#O
X
O
S
0₂
OSO
O<O C
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An adventure company runs two obstacle courses, Fundash and Coolsprint,
with similar designs. Since Fundash was built on rougher terrain, the
designer of the courses suspects that the mean completion time of Fundash
is greater than the mean completion time of Coolsprint. To test this, she
selects 230 Fundash runners and 275 Coolsprint runners. (Consider these as
independent random samples of the Fundash and Coolspring runners.) The
230 Fundash runners complete the course with a mean time of 78.5 minutes
and a standard deviation of 8.1 minutes. The 275 individuals complete
Coolsprint with a mean time of 76.7 minutes and a standard deviation of 6.5
minutes. Assume that the population standard deviations of the completion
times can be estimated to be the sample standard deviations, since the
samples that are used to compute them are quite large. At the 0.01 level of
significance, is there enough evidence to support the claim that the mean
completion time, ₁, of Fundash is greater than the mean completion time,
H₂, of Coolsprint? Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to at least three decimal places. (If
necessary, consult a list of formulas.)
(a) State the null hypothesis Ho and the alternative hypothesis H₁.
HO
H₁:0
(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.)
Espanol
(d) Find the p-value. (Round to three or more decimal places.)
(e) Can we support the claim that the mean completion time of Fundash is
greater than the mean completion time of Coolsprint?
OYes O No
H
X
■
a
S
X
2
0#0 O<O
Р
ê
ロ=ロ OSO 020
S
Olo
0
O>0

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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