교과서 질문
Finding a P-Value In Exercises 13–18, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance alpha.
Left-tailed test
z=-1.68
alpha=0.05
127
views
Ch. 7 - Hypothesis Testing with One Sample
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
Not the one you use?Change textbookSelect a different textbook
Table of contents
- 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: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
7장, 문제 7.5.20
In Exercises 15–22, test the claim about the population variance or standard deviation at the level of significance Assume the population is normally distributed.
Claim: σ^2>19, α=0.1. Sample statistics: s^2=28, n=17
검증된 단계별 안내1
Step 1: Identify the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is H₀: σ² ≤ 19, and the alternative hypothesis is H₁: σ² > 19. This is a right-tailed test because the claim is that the population variance is greater than 19.
Step 2: Determine the test statistic formula for a chi-square test for variance. The formula is χ² = ((n - 1) * s²) / σ₀², where n is the sample size, s² is the sample variance, and σ₀² is the hypothesized population variance.
Step 3: Substitute the given values into the formula. Here, n = 17, s² = 28, and σ₀² = 19. Compute the test statistic χ² using these values.
Step 4: Determine the critical value for the chi-square distribution at the given significance level α = 0.1 and degrees of freedom (df = n - 1). Use a chi-square distribution table or statistical software to find the critical value for df = 16.
Step 5: Compare the calculated test statistic to the critical value. If the test statistic is greater than the critical value, reject the null hypothesis H₀. Otherwise, fail to reject H₀. Interpret the result in the context of the claim.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Population Variance and Standard Deviation
Population variance (σ²) measures the spread of a set of values in a population, while the standard deviation (σ) is the square root of the variance. These metrics are crucial for understanding the variability within a dataset. In hypothesis testing, they help determine if observed data significantly deviates from a hypothesized value.
추천 영상:
가이드 코스
08:45
Calculating Standard Deviation
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 this case, the null hypothesis would state that the population variance is less than or equal to 19.
추천 영상:
가이드 코스
06:21Step 1: Write Hypotheses
Level of Significance (α)
The level of significance (α) is the probability of rejecting the null hypothesis when it is actually true, commonly set at 0.05 or 0.1. In this scenario, α=0.1 indicates a 10% risk of concluding that the population variance exceeds 19 when it does not. This threshold helps determine the critical value for making decisions in hypothesis testing.
추천 영상:
03:33Finding Binomial Probabilities Using TI-84 Example 1
관련 실천
교과서 질문
Graphical Analysis In Exercises 21 and 22, state whether each standardized test statistic z allows you to reject the null hypothesis. Explain your reasoning.
a. z = -1.301
b. z = 1.203
c. z = 1.280
d. z = 1.286
69
views
교과서 질문
Deciding on a Distribution In Exercises 31 and 32, decide whether you should use the standard normal sampling distribution or a t-sampling distribution to perform the hypothesis test. Justify your decision. Then use the distribution to test the claim. Write a short paragraph about the results of the test and what you can conclude about the claim.
Tuition and Fees An education publication claims that the mean in-state tuition and fees at public four-year institutions by state is more than \(10,500 per year. A random sample of 30 states has a mean in-state tuition and fees at public four-year institutions of \)10,931 per year. Assume the population standard deviation is \$2380. At α=0.01, test the publication’s claim.
49
views
교과서 질문
Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.
Phone Repairs A cell phone repair shop advertises that the mean cost of repairing a phone screen is less than \$120.
216
views
교과서 질문
Writing Hypotheses: Medicine A medical research team is investigating the mean cost of a 30-day supply of a heart medication. A pharmaceutical company thinks that the mean cost is less than \$60. You want to support this claim. How would you write the null and alternative hypotheses?
66
views
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.
Right-tailed test, α=0.05, n=23
77
views