Skip to main content
Ch. 8 - Hypothesis Testing
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 8 - Hypothesis Testing문제 8.4.8
8장, 문제 8.4.8

Testing Claims About Variation
In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population.


Birth Weights A simple random sample of birth weights of 30 girls has a standard deviation of 829.5 g. Use a 0.01 significance level to test the claim that birth weights of girls have the same standard deviation as birth weights of boys, which is 660.2 g (based on Data Set 6 “Births” in Appendix B).

검증된 단계별 안내
1
Step 1: Define the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis states that the standard deviation of birth weights for girls is equal to that of boys (σ = 660.2 g). The alternative hypothesis states that the standard deviation of birth weights for girls is not equal to that of boys (σ ≠ 660.2 g).
Step 2: Identify the test statistic to use. Since this is a test about the population standard deviation, use the chi-square test for variance. The test statistic is given by the formula: χ² = ((n - 1) * s²) / σ₀², where n is the sample size, s is the sample standard deviation, and σ₀ is the hypothesized population standard deviation.
Step 3: Calculate the degrees of freedom (df). The degrees of freedom for the chi-square test is given by df = n - 1, where n is the sample size. In this case, n = 30, so df = 30 - 1 = 29.
Step 4: Determine the critical value(s) or P-value. Since this is a two-tailed test (σ ≠ 660.2 g), find the critical chi-square values for a significance level of 0.01 and df = 29. Use a chi-square distribution table or statistical software to find these values. Alternatively, calculate the P-value based on the test statistic.
Step 5: Compare the test statistic to the critical value(s) or compare the P-value to the significance level (α = 0.01). If the test statistic falls outside the range of the critical values or if the P-value is less than 0.01, reject the null hypothesis. Otherwise, fail to reject the null hypothesis. State the conclusion in the context of the problem: whether there is sufficient evidence to support the claim that the standard deviation of birth weights for girls is different from that of boys.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m
도움이 되었나요?

주요 개념

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

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a statement of no effect or no difference, and the alternative hypothesis (H1), which indicates the presence of an effect or difference. The goal is to determine whether there is enough evidence in the sample data to reject the null hypothesis in favor of the alternative.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

P-value

The P-value is a measure that helps determine the strength of the evidence against the null hypothesis. It represents the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. A smaller P-value indicates stronger evidence against the null hypothesis, and if it is less than the predetermined significance level (e.g., 0.01), the null hypothesis is rejected.
추천 영상:
가이드 코스
06:50
Step 3: Get P-Value

Standard Deviation and Variance

Standard deviation is a statistic that quantifies the amount of variation or dispersion in a set of data values. It is the square root of the variance, which measures the average squared deviation of each data point from the mean. In hypothesis testing, comparing the standard deviations of two groups (e.g., birth weights of girls and boys) can help assess whether there is a significant difference in variability between the two populations.
추천 영상:
가이드 코스
08:45
Calculating Standard Deviation
관련 실천
교과서 질문

Test Statistics

In Exercises 9–12, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 to select the correct expression for evaluating the test statistic.)


Exercise 5 “Landline Phones”

128
views
교과서 질문

Interpreting P-value The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p > 0.5 which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer as a result in your hypothesis test: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why?

188
views
교과서 질문

Final Conclusions

In Exercises 21–24, use a significance level of α = 0.05 and use the given information for the following:


State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

Without using technical terms or symbols, state a final conclusion that addresses the original claim


Original claim: More than 35% of air travelers would choose another airline to have access to inflight Wi-Fi. The hypothesis test results in a P-value of 0.00001.

165
views
교과서 질문

Exact Method For each of the three different methods of hypothesis testing (identified in the left column), enter the P-values corresponding to the given alternative hypothesis and sample data. Use a 0.05 significance level. Note that the entries in the last column correspond to the Chapter Problem. How do the results agree with the large sample size?

180
views
교과서 질문

Type I and Type II Errors

In Exercises 25–28, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.)


The proportion of drivers who make angry gestures is greater than 0.25.

119
views
교과서 질문

Finding P-Values

In Exercises 13–16, do the following:


i. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

ii. Find the P-value. (See Figure 8-3.)

iii. Using a significance level of α = 0.05 should we reject H0 or should we fail to reject H0?


The test statistic of z = -0.75 is obtained when testing the claim that p<1/3.

165
views