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 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
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

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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2:53 minutes

Problem 8.CQQ.2

Textbook Question

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

Verified step by step guidance

Step 1: Identify the type of hypothesis test being conducted. Determine whether it is a one-sample test, two-sample test, or another type of test (e.g., t-test, z-test, chi-square test). This information is crucial for selecting the correct test statistic formula.

Step 2: Define the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis typically represents no effect or no difference, while the alternative hypothesis represents the claim being tested.

Step 3: Gather the necessary data for the test. This includes sample size (n), sample mean (x̄), population mean (μ), standard deviation (σ or s), and any other relevant parameters depending on the test type.

Step 4: Select the appropriate formula for the test statistic based on the type of test. For example, for a z-test, the formula is

\frac{(x_{¯} - μ)}{\frac{σ}{\sqrt{n}}}

, and for a t-test, the formula is

\frac{(x_{¯} - μ)}{\frac{s}{\sqrt{n}}}

. Ensure you use the correct formula for the given scenario.

Step 5: Plug the values from the data into the formula and simplify the expression to compute the test statistic. This value will be used to compare against the critical value or p-value to make a decision regarding the hypothesis.

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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 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 process includes calculating a test statistic, which helps assess the strength of the evidence against H0.

Test Statistic

A test statistic is a standardized value that is calculated from sample data during a hypothesis test. It quantifies the difference between the observed sample statistic and the hypothesized population parameter, relative to the variability in the sample. Common test statistics include the z-score for large samples and the t-score for smaller samples, each used to determine the significance of the results.

Significance Level

The significance level, often denoted as alpha (α), is the threshold used to determine whether to reject the null hypothesis. It represents the probability of making a Type I error, which occurs when the null hypothesis is incorrectly rejected. Common significance levels are 0.05 and 0.01, indicating a 5% or 1% risk of concluding that a difference exists when there is none.

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Related Practice

Textbook Question

Independent Samples Which of the following involve independent samples?

c. Data Set 1 “Body Data” includes a sample of pulse rates of 147 women and a sample of pulse rates of 153 men.

Textbook Question

Statistical Literacy and Critical Thinking

In Exercises 1–4, use the results from a Hankook Tire Gauge Index survey of a simple random sample of 1020 adults. Among the 1020 respondents, 86% rated themselves as above average drivers. We want to test the claim that more than 3/4 of adults rate themselves as above average drivers.

Number and Proportions

a. Identify the actual number of respondents who rated themselves as above average drivers.

Textbook Question

At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.

b. For random samples of size 860, what sample proportions of male births are at least as extreme as the sample proportion of 426/860?

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.

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?

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?

Textbook Question

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.

Textbook Question

In Exercises 5–16, use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.

Heights of Presidents A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (cm) of presidents along with the heights of their main opponents (from Data Set 22 “Presidents” in Appendix B).

a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights of presidents and their main opponents, the differences have a mean greater than 0 cm.

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