Domanda del libro di testo
Which statistic is the best unbiased estimator for μ?
a. s
b. xbar
c. the median
d. the mode
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Ch. 6 - Confidence Intervals
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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TOC.tableOfContents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 6.7
In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.
μ<33
Guida verificata passo dopo passo1
Identify the given claim: The claim is μ < 33, which is a statement about the population mean being less than 33.
Understand the complement of the claim: The complement of μ < 33 is μ ≥ 33. This is because the complement includes all values not covered by the original claim.
Determine the null hypothesis (Ho): The null hypothesis is the complement of the claim, which is μ ≥ 33. The null hypothesis typically represents the status quo or no effect.
Determine the alternative hypothesis (Ha): The alternative hypothesis is the claim itself, which is μ < 33. The alternative hypothesis represents the researcher's assertion or the statement being tested.
Summarize the hypotheses: Ho: μ ≥ 33 and Ha: μ < 33. These hypotheses are mutually exclusive and collectively exhaustive, ensuring all possibilities are covered.
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Null Hypothesis (H0)
The null hypothesis (H0) is a statement that indicates no effect or no difference, serving as a default position in statistical testing. In this context, it typically represents the status quo or a claim that a population parameter, such as the mean (μ), is equal to a specific value. For the given claim μ < 33, the null hypothesis would be H0: μ ≥ 33.
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Percorso guidato
06:21
Step 1: Write Hypotheses
Alternative Hypothesis (Ha)
The alternative hypothesis (Ha) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. It represents what the researcher aims to support through evidence. In this case, since the claim is μ < 33, the alternative hypothesis would be Ha: μ < 33, indicating that the population mean is indeed less than 33.
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Percorso guidato
06:21Step 1: Write Hypotheses
Complement of a Hypothesis
The complement of a hypothesis refers to the opposite scenario of the original claim. In hypothesis testing, if the null hypothesis states that a parameter is greater than or equal to a certain value, its complement would assert that the parameter is less than that value. For the claim μ < 33, the complement would be μ ≥ 33, which aligns with the null hypothesis.
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Percorso guidato
4:23Complementary Events
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In Exercises 21–24, construct the indicated confidence interval for the population mean μ.
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In Exercises 29–32, determine the minimum sample size n needed to estimate for the values of c, σ, and E.
c = 0.95, σ = 2.5, E = 1.
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In Exercises 9–12, construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.
c = 0.98, xbar = 4.3, s = 0.34, n = 14
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