Body Temperature The given expression is used for determining the...

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- Introduction to Confidence Intervals
  15m
- Confidence Intervals for Population Mean
  48m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample1h 1m
- Steps in Hypothesis Testing
  1h 1m
10. Hypothesis Testing for Two Samples2h 8m
11. Correlation48m
- Scatterplots & Intro to Correlation
  26m
- Correlation Coefficient
  21m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

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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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) )