Coffee and Depression: Researchers conducted a study investigating the relationship betweencaffeinated coffee consumption and risk of depression in women. They collected data on 50,739women free of depression symptoms at the start of the study in the year 1996, and these womenwere followed through 2006. The researchers used questionnaires to collect data on caffeinatedcoffee consumption, asked each individual about physician-diagnosed depression, and also askedabout the use of antidepressants. The table below shows the distribution of incidences of depressionby amount of caffeinated coffee consumption. (M. Lucas et al, 2011).Tip: Do NOT include the TOTAL row and column in your table when you copy into your technologyapplication such as Statcrunch or a Calculator.≤ 1 cup/week 2-6 cups/week 1 cup/day 2-3 cups/day ≥ 4 cups/day Total373905564952607Clinical Depression: Yes 670Clinical Depression: No 1154562441632911726228848132Total12215661717234 12290238350739

Solution :- a) We would use a chi-square test to evaluate if there is independence between…

Answered: Coffee and Depression: Researchers…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children with autism and children with typical development. The table below shows the number of mothers in each group who did and did not use prenatal vitamins during the three months before pregnancy (periconceptional period). Autism. No Autism Vitamins - Yes 143 Vitamins - No 111 159 70 Do we have sufficient evidence to conclude that the proportion of children with autism is different between women that used vitamins and women that did not if the type I error rate you are willing to tolerate is 5%? Not able to determine We should accept the null We should reject the null We should not reject the null
Eighteen participants took part in an experimental study that consisted of three levels: normal classroom teaching, normal classroom teaching with tutors, and an experimental teaching method to increase student scores on a statistics exam. Your data set includes the following variables: Treatment (1 - normal classroom teaching; 2 - normal classroom teaching with tutors; 3 - experimental teaching method) Gender (1 – female; 2 – male) Pre-test score (higher scores represent better student performance on a statistics exam) Post-test score (higher scores represent better student performance on a statistics exam) Stanford-Binet Intelligence Test scores (IQ) The number of hours the student studied per week. Do test scores at pre-treatment differ from test scores at post-treatment? Note, this analysis should be conducted ignoring the treatment group they are in. Select an appropriate statistical test and state teh hullhypothesis.
A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 2121 dieters, are chosen for the study. Group A is required to follow a specific diet and exercise regimen, and also take a 500500-mg supplement of calcium each day. Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 14.314.3 pounds with a standard deviation of 1.21.2 pounds. The members of Group B had lost a mean of 12.112.1 pounds with a standard deviation of 2.42.4 pounds during the same time period. Assume that the population variances are not the same. Construct a 99%99% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. Let Population 1 be the amount of weight lost by Group A, who took a 500500-mg supplement of calcium each day,…
Labor Day was created by the U.S. labor movement over 100 years ago. It was subsequently adopted by most states as an official holiday. In a poll by Gallup, 1000 randomly selected adults were asked whether they approve of labor unions; 650 said yes. In 1936, about 72% of Americans approved of labor unions. At a 5% level of significance, do the data provide sufficient evidence to conclude that the percentage of Americans who approve of labor unions now has decreased since 1936? Solve using the critical-value approach. Define the parameter we are testing and setup a hypothesis test to see if less than 72% of Americans approve of labor unions currently. Calculate the test statistics for this hypothesis test. What is the critical value for this hypothesis test?
In 2010, Dr. Bob decided to gather research on the type of disorders that present among his patients. His data collection resulted in the following breakdown of patients by disorder: 54.9% Schizophrenia; 21.1% Major Depression; 7.9% Obsessive-Compulsive Disorder; 4.5% Anxiety Disorder; 2.9% Personality Disorder; 8.8% Other. Information was collected from a random sample Of 300 patients in 2018 to determine whether or not the data has changed significantly. The sample data is given in the table below. At the a = 0.10 level of significance, test the claim that the disorder breakdown of patients at Dr. Bob's hospital has not changed significantly since 2010. Which would be correct hypotheses for this test? Ho: P1 = P2; H₁: P₁ P2 © Ha: t1 = Uz; Hư:1# 02 ⒸHO: The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits); H₁: The breakdwon of patients by disorder has not changed significantly since 2010 (i.e. the given distribution…
One study of cell phones and the risk of brain cancer looked at a group of 469 people who have brain cancer. The investigators then asked about the use of cell phones. Result: “Our data suggest that the use of hand- held cellular phones is not associated with risk of brain cancer. B . Based on this study, can you determine that cellular use does not CAUSE brain cancer? Why or why not?
The Wall Street Journal asked Concur Technologies, Inc., an expense management company, to examine data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city. The following table shows the average daily hotel room rate (X) and the average amount spent on entertainment (Y) for a random sample of 9 of the 25 most-visited U.S. cities. These data lead to the estimated regression equation y = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B. (NEED ANSWER FOR A) a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).
An important issue is whether there are racial differences in hypertension among children. We define hypertension as being above the 95th percentile for either systolic blood pressure (SBP) or diastolic blood pressure (DBP) among children of the same age, height, and sex. Since some of the children were observed at multiple visits, a GEE model was run of hypertension on ethnic group. There were three ethnic groups considered: Caucasian, African American, and Hispanic. The results among boys are given in Table 13.54. TABLE 13.54 Relationship between hypertension and ethnic group among 27,009 boys in the Pediatric Task Force Data Variable Regression Coefficient SE Intercept -2.07 0.026 African American 0.049 0.041 Hispanic 0.328 0.059 What is the estimated OR for hypertension comparing Hispanic boys vs. Caucasian boys? (Call this OR1.) What is a 95% CI for this estimate?
A sports psychologist studied the effect of a motivational program on number of injuries in one year among players of three different sports (baseball, football, and basketball). Players were randomly assigned to one of two conditions: either participate in a motivational program or none (control). Data was collected on the number of injuries sustained by each athlete that season. Question: If p = .024 for the main effect of sports, what should the researcher conclude?
Studies indicate that excessive noise at night can affect weight gain. One study of n = 127 rats compared the weight gain of rats exposed to excessive noise at night and the weight gain of rats in a quiet night environment. Sample statistics for the study are given in the table below. Use this information to determine if there is significant evidence that weight gain of rats exposed to excessive noise at night is different on average than weight gain of rats in a quiet night environment. Excessive noise at night environment (Group 1) Quiet night environment (Group 2) Sample mean (grams) 22.4 19.9 Sample standard deviation (grams) 6.4 3.8 Observations/Sample size 69 58 The p-value for this test is 0.0086. Make a decision and conclusion for the hypothesis test in context. Use a 5% significance level (α = 0.05).
Is gender independent of education level ? A random sample of 395 people were surveyed and each person was asked to report the highest education level they obtained .The data that resulted from the survey is summarized in the following table: High School Bachelors Masters PhD. Female 60 54 46 41 Male 40 44 53 57 Question: Are gender and education level dependent at 5percent level of significance ? In other words given the data collected above is there a relationship between the gender of an individual and the level of education that they have obtained ?
Attractiveness of body types has been a large discussion relating to effects on youth and culture. Unhealthy levels of BMI are often associated with beauty. A researcher decided to study how young heterosexual adults body type preferences related to BMI. Participants were asked to use a computer program to design their desired partner. The program then calculated the BMI of the designed partners. The table summarizes the results based on a SRS of 35 men and 48 women. BMI designed by men n=35 x-bar=18.850 stdev=1.750 SE Mean 0.277 BMI designed by women n=48 x-bar=25.860 stdev=4.215 SE Mean 0.625 Use this information to conduct a test to decide if male and/or female body type preferences are associated with healthy BMI measurements. You should have two complete tests here. You may assume the populations are normally distributed.

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