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Chapter 10: Problem 8

A researcher speculates that because of differences in diet, Japanese children may have a lower mean blood cholesterol level than U.S. children do. Suppose that the mean level for U.S. children is known to be 170 . Let \(\mu\) represent the mean blood cholesterol level for all Japanese children. What hypotheses should the researcher test?

Short Answer

Expert verified
The hypotheses that the researcher should test are H0: \(\mu = 170\) and H1: \(\mu < 170\).

Step by step solution

01

Formulate the Null Hypothesis (H0)

The null hypothesis assumes that the mean cholesterol level for Japanese children is equal to that of US children which is 170. Thus, H0: \(\mu = 170\)
02

Formulate the Alternative Hypothesis (H1)

The alternative hypothesis is what the researcher believes, which is that Japanese children have a lower mean blood cholesterol level than 170. Thus, H1: \(\mu < 170\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Null Hypothesis
The null hypothesis is like the starting point in statistical hypothesis testing. It assumes that there is no significant difference or effect. In this exercise, the null hypothesis is that the mean blood cholesterol level of Japanese children is the same as that of U.S. children, which is 170.

This hypothesis is commonly abbreviated as \( H_0 \) and is stated as \( \mu = 170 \). It serves as a baseline to evaluate whether there is enough evidence to suggest that Japanese children differ in their mean cholesterol levels compared to U.S. children.
  • Represents the status quo or what is assumed to be true unless proven otherwise.
  • Subject to testing to provide statistical evidence.
  • If data show enough evidence against it, we reject the null hypothesis.
Alternative Hypothesis
The alternative hypothesis reflects the researcher's theory or claim and is used to challenge the null hypothesis. It suggests that there is a significant effect or difference. In this context, the researcher proposes that Japanese children have a lower mean blood cholesterol level than 170, which is the known level for U.S. children.

This is represented as \( H_1 \) and formulated as \( \mu < 170 \).
  • Represents what the researcher is trying to demonstrate or prove.
  • If evidence supports it, we accept the alternative hypothesis.
  • It's considered only if the null hypothesis is rejected.
Mean Blood Cholesterol Level
The mean blood cholesterol level is the average amount of cholesterol present in the blood of a specific group. It plays a crucial role in determining the overall health and dietary impacts on a population. In this exercise, it's used as a comparative measure between Japanese and U.S. children.

Knowing the average cholesterol level (like the 170 for U.S. children) allows researchers to assess whether dietary habits might lead to differences in health outcomes between populations.
  • Indicator of cardiovascular health.
  • Helps identify trends or issues related to diet and lifestyle.
  • Used in hypothesis testing to compare two groups.
Japanese and U.S. Children Comparison
Comparing Japanese and U.S. children in terms of mean blood cholesterol levels provides insights into the effects of different dietary habits. The researcher suspects that Japanese children might have a healthier cholesterol level due to their diet. This is evaluated by statistical hypothesis testing.

The setup aims to examine potential differences, giving a clearer picture of how diet may influence children's health across different cultures.
  • Helps understand the impacts of cultural dietary practices.
  • Uses statistical methods to verify assumptions.
  • Can lead to further research and health guidelines.

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Most popular questions from this chapter

The article "Theaters Losing Out to Living Rooms" (San Luis Obispo Tribune, June 17,2005\()\) states that movie attendance declined in \(2005 .\) The Associated Press found that 730 of 1000 randomly selected adult Americans preferred to watch movies at home rather than at a movie theater. Is there convincing evidence that the majority of adult Americans prefer to watch movies at home? Test the relevant hypotheses using a .05 significance level.

The power of a test is influenced by the sample size and the choice of significance level. a. Explain how increasing the sample size affects the power (when significance level is held fixed). b. Explain how increasing the significance level affects the power (when sample size is held fixed).

A comprehensive study conducted by the National Institute of Child Health and Human Development tracked more than 1000 children from an early age through elementary school (New york Times, November 1,2005\()\). The study concluded that children who spent more than 30 hours a week in child care before entering school tended to score higher in math and reading when they were in the third grade. The researchers cautioned that the findings should not be a cause for alarm because the effects of child care were found to be small. Explain how the difference between the sample mean math score for third graders who spent long hours in child care and the known overall mean for third graders could be small but the researchers could still reach the conclusion that the mean for the child care group is significantly higher than the overall mean for third graders.

Give as much information as you can about the \(P\) -value of a \(t\) test in each of the following situations: a. Two-tailed test, \(\mathrm{df}=9, t=0.73\) b. Upper-tailed test, \(\mathrm{df}=10, t=-0.5\) c. Lower-tailed test, \(n=20, t=-2.1\) d. Lower-tailed test, \(n=20, t=-5.1\) e. Two-tailed test, \(n=40, t=1.7\)

The article "Poll Finds Most Oppose Return to Draft, Wouldn't Encourage Children to Enlist" (Associated Press, December 18,2005 ) reports that in a random sample of 1000 American adults, 700 indicated that they oppose the reinstatement of a military draft. Is there convincing evidence that the proportion of American adults who oppose reinstatement of the draft is greater than two-thirds? Use a significance level of .05 .
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