Students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Assume that a simple random sample has been selected. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute? 71 79 38 66 43 21 60 64 65 46 64 71 98 91 66 Question content area bottom Part 1 Perform the test assuming that the requirements are met. Identify the null and alternative hypotheses. H0: ▼ sigmaσ pp muμ ▼ less than< not equals≠ equals= greater than> enter your response here H1: ▼ pp muμ sigmaσ ▼ less than< greater than> not equals≠ equals= enter your response here (Type integers or decimals. Do not round.) Part 2 Identify the test statistic. enter your response here (Round to two decimal places as needed.) Part 3 Identify the P-value. enter your response here (Round to three decimal places as needed.) Part 4 State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Decide whether it appears that students are reasonably good at estimating one minute. ▼ Accept Fail to reject Reject the null hypothesis. There ▼ is not is sufficient evidence at the 0.05 significance level to ▼ warrant rejection of support the claim that the times are from a population with a mean equal to 60 seconds; on this basis it ▼ does not appear appears that as a group the students are reasonably good at estimating one minute.

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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Question content area bottom

Part 1

Perform the test assuming that the requirements are met. Identify the null and alternative hypotheses.

H0:

▼

sigmaσ

muμ

▼

less than<

not equals≠

equals=

greater than>

enter your response here

H1:

▼

muμ

sigmaσ

▼

less than<

greater than>

not equals≠

equals=

enter your response here

(Type integers or decimals. Do not round.)

Part 2

Identify the test statistic.

enter your response here

(Round to two decimal places as needed.)

Part 3

Identify the P-value.

enter your response here

(Round to three decimal places as needed.)

Part 4

State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Decide whether it appears that students are reasonably good at estimating one minute.

▼

Fail to reject

Reject

the null hypothesis. There

▼

is not

sufficient evidence at the

0.05

significance level to

▼

warrant rejection of

support

the claim that the times are from a population with a mean equal to

seconds; on this basis it

▼

does not appear

appears

that as a group the students are reasonably good at estimating one minute.

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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