A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.10 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? A. Determine the test statistic. (Round to two decimal places as needed.) B. Determine the P-value.(Round to three decimal places as needed.) **Data Set**The following series of numbers represents a data set that can be used for statistical analysis:- 72- 81- 42- 64- 45- 25- 61- 63- 64- 46- 62- 70- 90- 87- 63**Usage**This data can be applied in various educational contexts, such as teaching statistical concepts like mean, median, mode, range, and standard deviation. The values can also be used in exercises related to data visualization, such as creating histograms, bar charts, or box plots.**Visualization Tips**For visual learners, consider using a bar graph to represent the frequency of each number in the set. This can help highlight the mode and observe any patterns or trends in the data. Using a line graph might help illustrate changes or trends if these numbers represent a time series or sequential data.**Data Analysis Questions**1. What is the mean of the data set?2. Identify the mode(s) of the data set.3. Calculate the median value.4. Determine the range of the values.5. Discuss how the data might be interpreted in a real-world context.

First we calculate the mean and standard deviation of the given data to find the test statistic

Answered: A group of students estimated the…

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

A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.10 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?

A. Determine the test statistic.

(Round to two decimal places as needed.)

B. Determine the P-value.

(Round to three decimal places as needed.)

**Data Set**

The following series of numbers represents a data set that can be used for statistical analysis:

- 72
- 81
- 42
- 64
- 45
- 25
- 61
- 63
- 64
- 46
- 62
- 70
- 90
- 87
- 63

**Usage**

This data can be applied in various educational contexts, such as teaching statistical concepts like mean, median, mode, range, and standard deviation. The values can also be used in exercises related to data visualization, such as creating histograms, bar charts, or box plots.

**Visualization Tips**

For visual learners, consider using a bar graph to represent the frequency of each number in the set. This can help highlight the mode and observe any patterns or trends in the data. Using a line graph might help illustrate changes or trends if these numbers represent a time series or sequential data.

**Data Analysis Questions**

1. What is the mean of the data set?
2. Identify the mode(s) of the data set.
3. Calculate the median value.
4. Determine the range of the values.
5. Discuss how the data might be interpreted in a real-world context.

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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