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Ch. 8 - Hypothesis Testing
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 8 - Hypothesis Testing문제 8.CQQ.3
8장, 문제 8.CQQ.3

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?

검증된 단계별 안내
1
Step 1: Identify the type of hypothesis test being conducted in Exercise 1. Typically, this involves determining whether the test is for a mean, proportion, variance, or other statistical parameter. The type of test will dictate the distribution used (e.g., t-distribution, z-distribution, chi-square distribution).
Step 2: Determine the sample size (n = 62) and whether the population standard deviation is known. If the population standard deviation is unknown and the sample size is small (n < 30), the t-distribution is used. If the sample size is large (n ≥ 30), the Central Limit Theorem allows the use of the z-distribution, even if the population standard deviation is unknown.
Step 3: Assess whether it is necessary to check for normality. For hypothesis tests involving means, if the sample size is large (n ≥ 30), the Central Limit Theorem ensures that the sampling distribution of the sample mean is approximately normal, regardless of the population's distribution. Therefore, checking for normality is not strictly necessary in this case.
Step 4: If the sample size were small (n < 30), it would be necessary to verify that the population from which the sample is drawn is approximately normal. This can be done using graphical methods (e.g., histograms, Q-Q plots) or statistical tests for normality (e.g., Shapiro-Wilk test).
Step 5: Conclude that for this specific problem, since the sample size is 62 (which is large), it is not necessary to determine whether the weights come from a population with a normal distribution. The Central Limit Theorem justifies the use of the z-distribution for the hypothesis test.

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주요 개념

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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject H0. The outcome is often assessed using a p-value, which indicates the probability of observing the sample data if H0 is true.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

Normal Distribution

A normal distribution is a continuous probability distribution characterized by its bell-shaped curve, defined by its mean and standard deviation. Many statistical tests, including t-tests and ANOVA, assume that the data follows a normal distribution. If the sample size is large enough, the Central Limit Theorem suggests that the sampling distribution of the sample mean will be approximately normal, regardless of the population's distribution.
추천 영상:
가이드 코스
09:47
Finding Standard Normal Probabilities using z-Table

Central Limit Theorem

The Central Limit Theorem (CLT) states that the distribution of the sample mean will approach a normal distribution as the sample size increases, regardless of the original population's distribution. This theorem is crucial for hypothesis testing because it allows statisticians to make inferences about population parameters using sample statistics, especially when dealing with large samples, even if the underlying data is not normally distributed.
추천 영상:
가이드 코스
04:52
Calculating the Mean
관련 실천
교과서 질문

Robust Explain what is meant by the statements that the t test for a claim about μ is robust, but the (chi)^2 test for a claim about σ is not robust.

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교과서 질문

Discarded Plastic Find the test statistic used for the hypothesis test described in Exercise 1.

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교과서 질문

Lightning Deaths The graph in Cumulative Review Exercise 5 was created by using data consisting of 242 male deaths from lightning strikes and 64 female deaths from lightning strikes. Assume that these data are randomly selected lightning deaths and proceed to test the claim that the proportion of male deaths is greater than . Use a 0.01 significance level. Any explanation for the result?

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교과서 질문

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?

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교과서 질문

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.

111
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교과서 질문

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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