Ch. 8 - Hypothesis Testing

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 8 - Hypothesis Testing

Problem 8.C.1f

Chapter 8, Problem 8.C.1f

Lightning Deaths Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of recent and consecutive years. Find the values of the indicated statistics.
46 51 44 51 43 32 38 48 45 27 34 29 26 28 23 26 28 40 16 20
f. What important feature of the data is not revealed from an examination of the statistics, and what tool would be helpful in revealing it? What does a quick examination of the data reveal?

Verified step by step guidance

Step 1: Begin by understanding the problem. We are given a list of numbers representing the deaths from lightning strikes in the United States over several years. We need to find the values of the indicated statistics and identify any important features not revealed by these statistics.

Step 2: Calculate basic statistics such as the mean, median, mode, range, variance, and standard deviation. These statistics provide a summary of the data's central tendency and variability.

Step 3: Consider the distribution of the data. Are there any outliers or unusual patterns? A quick examination of the data can reveal if the numbers are generally consistent or if there are any years with significantly higher or lower deaths.

Step 4: Identify what the statistics might not reveal. For example, statistics like mean and median do not show the distribution shape or any potential outliers. A histogram or box plot could be helpful tools to visualize the data distribution and identify any outliers or skewness.

Step 5: Reflect on the data's context. A quick examination of the data might reveal trends, such as a decrease in deaths over time, which could be due to improved safety measures or other factors. This context is important for interpreting the statistics meaningfully.

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Key Concepts

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

Descriptive Statistics

Descriptive statistics involve summarizing and organizing data to describe its main features. Common measures include mean, median, mode, and standard deviation, which provide insights into the central tendency and variability of the data. In the context of lightning deaths, these statistics help understand the average number of deaths and the spread of data over the years.

Data Visualization

Data visualization is the graphical representation of data, which helps in identifying patterns, trends, and outliers that may not be evident from raw data or summary statistics alone. Tools like histograms, box plots, or scatter plots can reveal the distribution and any anomalies in lightning death data, offering a clearer picture of its behavior over time.

Outliers

Outliers are data points that differ significantly from other observations, potentially indicating variability or errors in data collection. Identifying outliers is crucial as they can skew results and affect statistical analyses. In the lightning deaths data, examining outliers can help understand unusual years with exceptionally high or low death counts, which may not be apparent from basic statistics.

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Related Practice

Textbook Question

Test Statistic and Critical Value The statistics for the sample data in Exercise 1 are n = 15, x_bar = 6.133333, and s = 8.862978, where the units are millions of dollars. Find the test statistic and critical value(s) for a test of the claim that the salaries are from a population with a mean greater than 5 million dollars. Assume that a 0.05 significance level is used.

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Textbook Question

Estimates vs. Hypothesis Tests Labels on cans of Dr. Pepper soda indicate that they contain 12 oz of the drink. We could collect samples of those cans and accurately measure the actual contents, then we could use methods of Section 7-2 for making an estimate of the mean amount of Dr. Pepper in cans, or we could use those measured amounts to test the claim that the cans contain a mean of 12 oz. What is the difference between estimating the mean and testing a hypothesis about the mean?

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Textbook Question

Discarded Plastic

What distribution is used for the hypothesis test described in Exercise 1?

For the hypothesis test described in Exercise 1, is it necessary to determine whether the 62 weights appear to be from a population having a normal distribution? Why or why not?

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Textbook Question

Final Conclusions

In Exercises 21–24, use a significance level of α = 0.05 and use the given information for the following:

State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: The mean pulse rate (in beats per minute) of adult males is 72 bpm. The hypothesis test results in a P-value of 0.0095.

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Textbook Question

Discarded Plastic Data Set 42 “Garbage Weight” includes weights (pounds) of discarded plastic from 62 different households. Those 62 weights have a mean of 1.911 pounds and a standard deviation of 1.065 pounds. We want to use a 0.05 level of significance to test the claim that this sample is from a population with a mean less than 2.000 pounds. Identify the null hypothesis and alternative hypothesis.

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Textbook Question

Discarded Plastic The P-value for the hypothesis test described in Exercise 1 is 0.2565.

What should be concluded about the null hypothesis?

What is the final conclusion that addresses the original claim?

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