Table of contents

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 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Previous problemNext problem

1:32 minutes

Problem 8.2.1a

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.

Verified step by step guidance

Step 1: Understand the problem. We are tasked with identifying the actual number of respondents who rated themselves as above average drivers. The survey provides the total number of respondents (1020) and the percentage of those who rated themselves as above average drivers (86%).

Step 2: Convert the percentage into a decimal. To do this, divide the percentage (86%) by 100. This gives the proportion of respondents who rated themselves as above average drivers.

Step 3: Multiply the total number of respondents (1020) by the decimal proportion obtained in Step 2. This will give the actual number of respondents who rated themselves as above average drivers.

Step 4: Write the formula for clarity: Actual number = Total respondents × Proportion. Substitute the values: Actual number = 1020 × (86/100).

Step 5: Perform the multiplication to find the actual number of respondents. This will give the final result, which represents the number of adults who rated themselves as above average drivers.

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Key Concepts

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

Simple Random Sample

A simple random sample is a subset of individuals chosen from a larger population, where each individual has an equal chance of being selected. This method ensures that the sample is representative of the population, minimizing bias and allowing for valid statistical inferences. In this context, the sample of 1020 adults provides a basis for analyzing the self-assessment of driving skills among the general adult population.

Proportion

A proportion is a statistical measure that represents the part of a whole, expressed as a fraction or percentage. In this case, 86% of the respondents rated themselves as above average drivers, which can be converted into a proportion by dividing the number of respondents who rated themselves as such by the total number of respondents. Understanding proportions is essential for interpreting survey results and making comparisons.

Hypothesis Testing

Hypothesis testing is a statistical method used to determine whether there is enough evidence to support a specific claim about a population parameter. In this scenario, the claim is that more than 3/4 (or 75%) of adults consider themselves above average drivers. By conducting a hypothesis test, we can evaluate this claim using the sample data and assess whether the observed proportion significantly exceeds the hypothesized value.

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Textbook Question

Can Dogs Detect Malaria? A study was conducted to determine whether dogs could detect malaria from socks worn by malaria patients and socks worn by patients without malaria. Among 175 socks worn by malaria patients, the dogs made correct identifications 123 times. Among 145 socks worn by patients without malaria, the dogs made correct identifications 131 times (based on data presented at an annual meeting of the American Society of Tropical Medicine, by principal investigator Steve Lindsay). Use a 0.05 significance level to test the claim of no difference between the two rates of correct responses.

c. What do the results suggest about the use of dogs to detect malaria?

Textbook Question

Independent Samples Which of the following involve independent samples?

a. Data Set 4 “Measured and Reported” includes measured heights matched with the heights that were reported when the subjects were asked for those values.

Textbook Question

Independent Samples Which of the following involve independent samples?

b. Data Set 6 “Births” includes birth weights of a sample of baby boys and a sample of baby girls.

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

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

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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