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Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Larson 8th EditionCh. 7 - Hypothesis Testing with One Sample문제 7.4.4
7장, 문제 7.4.4

In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.
Claim: p ≥0.48, α=0.08. Sample statistics: p_hat = 0.40, n=90

검증된 단계별 안내
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Step 1: Verify the conditions for using a normal sampling distribution. The two conditions are: (1) The sample size n must be large enough such that both n * p and n * (1 - p) are greater than or equal to 5, and (2) the sampling must be random and independent.
Step 2: Calculate n * p and n * (1 - p) using the claimed population proportion p = 0.48 and sample size n = 90. Use the formulas: n * p and n * (1 - p).
Step 3: Check if both n * p and n * (1 - p) are greater than or equal to 5. If they are, then the normal approximation can be used. If not, the normal approximation cannot be used.
Step 4: If the normal approximation is valid, calculate the test statistic z using the formula: z = (p̂ - p) / sqrt((p * (1 - p)) / n), where p̂ is the sample proportion, p is the claimed proportion, and n is the sample size.
Step 5: Compare the calculated z-value to the critical z-value for the given significance level α = 0.08 in a one-tailed test. Determine whether to reject or fail to reject the null hypothesis based on this comparison.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Normal Sampling Distribution

A normal sampling distribution is applicable when the sample size is sufficiently large, typically n ≥ 30, and the population proportion is not too close to 0 or 1. This allows the sampling distribution of the sample proportion (p_hat) to be approximated by a normal distribution, facilitating hypothesis testing and confidence interval estimation.
추천 영상:
05:11
Sampling Distribution of Sample Proportion

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample statistics to determine whether to reject H0 in favor of H1, based on a predetermined significance level (α).
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

Sample Proportion (p_hat)

The sample proportion (p_hat) is the ratio of the number of successes in a sample to the total number of observations in that sample. It serves as an estimate of the population proportion (p) and is crucial for conducting hypothesis tests regarding population proportions, especially when comparing it to a claimed value.
추천 영상:
05:11
Sampling Distribution of Sample Proportion
관련 실천
교과서 질문

Hypothesis Testing Using Rejection Region(s) In Exercises 39–44, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.


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교과서 질문

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.


Left-tailed test, α=0.10, n=20

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교과서 질문

What are the two types of hypotheses used in a hypothesis test? How are they related?

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교과서 질문

A travel analyst claims the mean daily base price for renting a full-size or less expensive vehicle in Vancouver, British Columbia, is more than \(86. You want to test this claim. In a random sample of 40 full-size or less expensive vehicles available to rent in Vancouver, British Columbia, the mean daily base price is \)93.23. Assume the population standard deviation is \$28.90. At α=0.10, do you have enough evidence to support the analyst’s claim?

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교과서 질문

A government agency reports that the mean amount of earnings for full-time workers ages 18 to 24 with a bachelor’s degree in a recent year is \(52,133. In a random sample of 15 full-time workers ages 18 to 24 with a bachelor’s degree, the mean amount of earnings is \)48,400 and the standard deviation is \$6679. At α=0.05, is there enough evidence to reject the claim? Assume the population is normally distributed.

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교과서 질문

[APPLET] A weight loss program claims that program participants have a mean weight loss of at least 10.5 pounds after 1 month. The weight losses after 1 month (in pounds) of a random sample of 40 program participants are listed below. At α=0.01, is there enough evidence to reject the program’s claim?


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