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Ch. 1 - Introduction to Statistics
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 1 - Introduction to StatisticsProblem 1.C.4
Chapter 1, Problem 1.C.4

Body Temperature The given expression is used for determining the likelihood that the average (mean) human body temperature is different from the value of 98.6°F that is commonly used. Find the given value and round the result to two decimal places.


(98.2 - 98.6) / (0.62 / sqrt(106) )

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1
Identify the components of the expression: the numerator is the difference between the sample mean and the population mean (98.2 - 98.6), and the denominator is the standard error of the mean, which is the sample standard deviation (0.62) divided by the square root of the sample size (106).
Calculate the numerator: Subtract the population mean (98.6) from the sample mean (98.2) to find the difference.
Calculate the denominator: First, find the square root of the sample size (106). Then, divide the sample standard deviation (0.62) by this square root value to find the standard error.
Form the test statistic: Divide the result from the numerator by the result from the denominator. This will give you the test statistic, which is a t-score in this context.
Round the test statistic to two decimal places to obtain the final value, which represents the likelihood that the average human body temperature is different from 98.6°F.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the population based on sample data. It involves comparing the sample mean to a known value, such as 98.6°F, to determine if there is a significant difference. This process helps in assessing whether observed data can be attributed to random chance or if there is evidence of a true effect.
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Step 1: Write Hypotheses

Standard Error

Standard error measures the variability of a sample mean from the population mean. It is calculated by dividing the sample standard deviation by the square root of the sample size, as seen in the expression (0.62 / sqrt(106)). A smaller standard error indicates that the sample mean is a more accurate reflection of the population mean, which is crucial for hypothesis testing.
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Calculating Standard Deviation

Z-Score

A Z-score represents the number of standard deviations a data point is from the mean. In the given expression, (98.2 - 98.6) / (0.62 / sqrt(106)), the Z-score is used to determine how far the sample mean of 98.2°F deviates from the hypothesized mean of 98.6°F. Calculating the Z-score helps in assessing the likelihood of observing such a sample mean under the null hypothesis.
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Z-Scores From Given Probability - TI-84 (CE) Calculator
Related Practice
Textbook Question

Determining Sample Size The given expression is used to determine the size of the sample necessary to estimate the proportion of college students who have the profound wisdom to take a statistics course. Find the value and round the result up to the next larger whole number.


[(1.95996)^2 - 0.25] / (0.03)^2

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Textbook Question

In Exercises 21–28, determine whether the study is an experiment or an observational study, and then identify a major problem with the study.

Drinking and Driving A researcher for a consortium of insurance companies plans to test for the effects of drinking on driving ability by randomly selecting 1000 drivers and then randomly assigning them to two groups: One group of 500 will drive in New York City after no alcohol consumption, and the second group will drive in New York City after consuming three shots of Jim Beam bourbon whiskey.

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Textbook Question

Discrete/Continuous Data Which of the following describe discrete data?


a. The exact heights of all NBA basketball players

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Textbook Question

IQ Scores Listed below are the IQ scores of randomly selected statistics professors. What value is obtained when those IQ scores are added and the total is divided by the number of scores? (This result, called the mean, is discussed in Chapter 3.) What is notable about these values?


135 149 145 129 118 119 115 133 107 188

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Textbook Question

In Exercises 37–44, answer the given questions, which are related to percentages.

Texting While Driving USA Today reported results from an Arity survey in which 2018 drivers were asked if they text while driving.


a. Among the respondents, 42% said that they text while driving. What is the exact value that is 42% of the number of respondents?

b. Could the result from part (a) be the actual number of respondents who said that they text while driving? Why or why not?

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Textbook Question

Standard Deviation One way to get a very rough approximation of the value of a standard deviation of sample data is to find the range, then divide it by 4. The range is the difference between the highest sample value and the lowest sample value. In using this approach, what value is obtained from the sample data listed in Exercise 1 “IQ Scores”?

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