/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 117 A study was recently reported co... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 117

A study was recently reported comparing the effects of different dietary patterns on blood pressure within an 8-week follow-up period [16]. Subjects were randomized to three groups: \(A,\) a control diet group, \(N=154 ; B,\) a fruits-andvegetables diet group, \(N=154 ; \mathrm{C},\) a combination-diet group consisting of a diet rich in fruits, vegetables, and lowfat dairy products and with reduced saturated and total fat, \(N=151 .\) The results reported for systolic blood pressure (SBP) are shown in Table 8.29. 8.117 Suppose we want to compute a two-sided \(p\) -value for this comparison. Without doing any further calculation, which statement(s) must be false? $$\text { (1) } p=.01(2) p=.04(3) p=.07(4) p=.20$$

Short Answer

Expert verified
Statement (4) p=.20 must be false if the results show significant differences.

Step by step solution

01

Understanding p-value and its significance

The p-value is a statistical measure that helps determine the significance of results from an experiment or study. A small p-value (typically 鈮� 0.05) indicates strong evidence against the null hypothesis, suggesting that it is unlikely that the observed data would occur if the null hypothesis were true.
02

Determining unlikely p-values

Given that the study is comparing dietary patterns' effects on blood pressure, the most likely goals of the study are to show differences between the groups. For a significant study like this, a p-value very close to zero, such as 0.01 or 0.04, would generally suggest significant differences. Conversely, a larger p-value like 0.20 indicates that differences are not statistically significant.
03

Identifying False Statements

To identify which of the given statements must be false, recall that smaller p-values denote significant results. Since larger p-values imply a lack of significant effect, p=0.20 must be false if we assume the study demonstrated some significant differences between diet groups.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding the Null Hypothesis
In any scientific study, the null hypothesis serves as a starting point for analysis. It posits that there is no effect or no difference, and any observed differences are due to random chance.
For the blood pressure study, the null hypothesis would claim that different dietary patterns have no effect on systolic blood pressure.
- This means the blood pressure change among the three diet groups (control, fruits-vegetables, combination) would not significantly differ.
- The goal of the study is to reject this hypothesis by showing evidence that dietary patterns do impact blood pressure.
Interpreting Statistical Significance and p-Values
Statistical significance relates closely to the concept of p-values. A p-value quantifies the probability of observing the test results, or more extreme, given that the null hypothesis is true.
- A p-value less than or equal to 0.05 is typically considered statistically significant. It suggests that the observed effect is unlikely due to random fluctuation.
- In the context of the blood pressure study, a p-value of 0.01 or 0.04 would indicate strong evidence that dietary patterns do affect systolic blood pressure, thus rejecting the null hypothesis.
- On the other hand, a p-value of 0.20 suggests the differences in blood pressure resulting from different diets are likely due to chance, hence not statistically significant.
Role of Dietary Patterns in the Study
Dietary patterns refer to the overall diet and the synergy between different food components. In the blood pressure study, three distinct diets were tested:
- **Control Diet:** Likely resembles a regular diet with no special focus on fruits, vegetables, or low-fat components.
- **Fruits-and-Vegetables Diet:** Focus on increasing intake of wholesome fruits and vegetables while possibly moderating other food intakes.
- **Combination Diet:** A mix of fruits, vegetables, low-fat dairy, and reduced fat intake aiming to optimize heart health.
Each of these diets was tested to observe their effects on blood pressure, identifying which pattern helps reduce systolic blood pressure most effectively.
Examining the Blood Pressure Study
Blood pressure, particularly systolic blood pressure (SBP), is a crucial metric in evaluating cardiovascular health. High blood pressure increases risks of heart disease and stroke. This study assesses:
- How different diets impact SBP after an 8-week period.
- Participants' blood pressure was measured and compared across three diet groups.
By using p-values to determine which dietary patterns have a statistically noticeable effect, the study sought to highlight beneficial food intake adjustments. The aim was not only to identify the most effective diet for lowering SBP but also to provide actionable dietary recommendations for improving cardiovascular health.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose we determine a \(95 \%\) Cl for the true mean change in pulmonary function on high-ozone days. Is this \(\mathrm{Cl}\) narrower, wider, or the same width as a \(90 \%\) Cl? (Do not actually compute the Cl.)

Age at menarche (onset of menstrual periods) is an important risk factor for breast cancer and possibly ovarian cancer. In general, women who reach menarche at an earlier age have a higher incidence of breast cancer. The longterm trend in developed countries is that age at menarche has been declining over the past 50 years. One hypothesis is that women with higher childhood SES have an earlier age at menarche. Suppose we identify 20 girls with low childhood SES (that is, head of household is a blue-collar worker) and find mean age at menarche of 13.4 years with a standard deviation of 1.4 years. We identify an additional 30 girls with high childhood SES (head of household is a white-collar worker or executive) and find a mean age at menarche of 12.9 years with a standard deviation of 1.5 years. Assume that the underlying variance of age at menarche for girls with low childhood SES and girls with high childhood SES is the same. 8.136 What test can be used to compare the mean of the two groups?

A study compared mean electroretinogram (ERG) amplitude of patients with different genetic types of retinitis pigmentosa (RP), a genetic eye disease that often results in blindness. The results shown in Table 8.24 were obtained for In (ERG amplitude) among patients \(18-29\) years of age. $$\begin{array}{lcc} \hline \text { Genetic type } & \text { Mean } \pm \mathrm{sd} & n \\ \hline \text { Dominant } & 0.85 \pm 0.18 & 62 \\ \text { Recessive } & 0.38 \pm 0.21 & 35 \\ \text { X-linked } & -0.09 \pm 0.21 & 28 \\ \hline \end{array}$$ What is the standard error of In(ERG amplitude) among patients with dominant RP? How does it differ from the standard deviation in the table?

A 1980 study was conducted whose purpose was to compare the indoor air quality in offices where smoking was permitted with that in offices where smoking was not permitted [7]. Measurements were made of carbon monoxide (CO) at 1:20 p.m. in 40 work areas where smoking was permitted and in 40 work areas where smoking was not permitted. Where smoking was permitted, the mean CO level was 11.6 parts per million (ppm) and the standard deviation CO was 7.3 ppm. Where smoking was not permitted, the mean CO was 6.9 ppm and the standard deviation CO was 2.7 ppm. Provide a \(95 \%\) Cl for the difference in mean CO between the smoking and nonsmoking working environments.

A study was conducted of genetic and environmental influences on cholesterol levels. The data set used for the study were obtained from a twin registry in Sweden [10]. Specifically, four populations of adult twins were studied: (1) monozygotic (MZ) twins reared apart, (2) MZ twins reared together, (3) dizygotic (DZ) twins reared apart, and (4) DZ twins reared together. One issue is whether it is necessary to correct for gender before performing more complex genetic analyses. The data in Table 8.17 were presented for total cholesterol levels for \(\mathrm{MZ}\) twins reared apart, by gender. If we assume (a) serum cholesterol is normally distributed, (b) the cholesterol levels within each sample consist of independent observations, and (c) the standard deviations for men and women are the same, then what is the name of the statistical procedure that can be used to compare the two groups?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.