Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

1. Intro to Stats and Collecting Data

Intro to Stats

Statistics

1. Intro to Stats and Collecting Data

Intro to Stats

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1:36 minutes

Problem 1.C.4

Textbook Question

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) )

Verified step by step guidance

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.

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.

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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Related Practice

Textbook Question

Percentages

b. In a Pew Research Center poll on driving, 58% of the 1182 respondents said that they like to drive. What is the actual number of respondents who said that they like to drive?

Textbook Question

Percentages

c. In a Pew Research Center poll on driving, 331 of the 1182 respondents said that driving is a chore. What percentage of respondents said that driving is a chore?

Textbook Question

Types of Data In each of the following, identify the level of measurement of the sample data (nominal, ordinal, interval, ratio) and the type of sampling used to obtain the data (random, systematic, convenience, stratified, cluster).

b. In each of the 50 states, 50 voters are randomly selected and their political party affiliations are identified.

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

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

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”?

Textbook Question

In Exercises 9–12, the given expressions are designed to yield results expressed in a form of scientific notation. For example, the calculator-displayed result of 1.23E5 can be expressed as 123,000, and the result of 1.23E-4 can be expressed as 0.000123. Perform the indicated operation and express the result as an ordinary number that is not in scientific notation.

(8)^12

Textbook Question

(0.2)^12

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