3.) Exercises chapter 3 & 4

- Consider the following cross-tabulation table from a 12-week study of diet

and exercise. Compute all of the marginal, conditional, and joint probabilities.

** **

**Weight Loss Strategy**

** **

**Diet and**

**Achievement of Goal Weight Diet Alone Exercise Total**

Did not achieve goal weight 80 40

Achieved goal weight 20 60

** **

**Total**

** **

- Consider the following cross-tabulation table from a national study of

women’s health. It seeks to examine the relationship between education level

and smoking. Compute all of the marginal, conditional, and joint probabilities.

**Smoking Status**

**Education Level Does Not Smoke ( n) Smokes (n) Total**

Less than high school degree 250 75

High school degree or GED 620 235

2-year college degree (AA/AS) 554 154

4-year college degree (BA/BS) 369 72

Postgraduate degree 167 23

(MA/MS/PhD/MD/JD)

**Total**

** **

- A large group of students take an examination (top score, 100), and the

results are normally distributed. The mean score on the examination is 82,

with a standard deviation of 6.58. A study group of four students obtain

scores of 78, 82, 88, and 95. For each score, compute the corresponding

z-score and find its percentile rank. Round the z-scores to the nearest hundredth

place.

- Data from 155 patients at a diabetes clinic include measures of their HbA1c

(a measure of how controlled blood sugar is). The mean HbA1c value is 8.2,

with a standard deviation of 1.3. Compute the 95% and 99% confidence

intervalsaroundthis mean.

- Read the article by Baibergenova A, Kudyakov R, Zdeb M, and Carpenter D.

(2003) titled “Low Birth Weight and Residential Proximity to PCBcontaminated

Waste Sites,” which can be found in *Environmental HealthPerspectives*, 111(i10), 1352–1358. Write the five hypotheses that this study istesting. Write both the null and alternative hypotheses for each one.

- Choose a research article from your field. Write the five hypotheses that this

study is testing. Write both the null and alternative hypotheses for each one.

- Imagine that you are going to conduct a study. Write the purpose of the

study, research questions, and main hypotheses. Write both the null and

alternative hypotheses for each one.

* *

* *

- Compute z-tests and find the one-tailed
*p-*value for each of the following situations.

Then write up the results of the analysis in a single sentence. Use

_ .05 as your definition of statistical significance.

- The mean BMI for U.S. men is 26.8, with a standard deviation of 4.6. You

have data from a sample of 25 men with type II diabetes who are attending

a diabetes health promotion program. The mean BMI of the sample is

31.3.

- The mean age for U.S. citizens is 45.2 years, with a standard deviation of

17.5 years. The 36 men in the sample have a mean age of 47 years.

- The average adult in the United States travels 40 miles each day (mostly

by car), with a standard deviation of 8.2 miles. You have data from a group

of 49 urban women who travel 38.2 miles each day.

- Compute t-tests and find the critical value using a two-tailed test and an _-

level of .05. State your conclusions.

- The standard for a good overall cholesterol level is 200 mg/dL or lower.

You have data from a group of 31 women athletes. Their overall cholesterol

is 178 mg/dL with a standard deviation of 18.2 mg/dL. Is their cholesterol

significantly different from this at *p * .05?

- The average child should consume about 2200 calories a day. You have

data from a group of 19 children who all watch more than 2 hours of television

a day. On average, they consume 2650 calories a day, with a standard

deviation of (122). Is their caloric intake significantly different from

that of other children at *p *.01?

- The target aerobic heart rate for people age 20 years is 120 bpm. You have

data from a group of 16 male golfers (all age 20 years). Their average heart

rate after golfing for 30 minutes is 110 bpm, with a standard deviation of

15.8 bpm. Is their golfing providing them with enough aerobic exercise?

Use an _-level of .01.

4.) Testable Hypothesis: is a form of hypothesis that can either be supported or else falsified from data or experience. It’s the type of hypothesis you want to state to conceive and perform an experiment using the scientific method.

My example of testable hypothesis: “People exposed to tobacco smoke have a higher incidence of cancer than the norm.”

A null hypothesis is a hypothesisdenoted by H_{0} that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove. A researcher is challenged by the null hypothesis and usually wants to disprove it, to demonstrate that there is a statistically-significant relationship between the two variables in the hypothesis. Nevertheless, an alternative hypothesis denoted by H_{1} or H_{a},simply is the inverse, or opposite, of the null hypothesis. It is the hypothesis that sample observations are influenced by some non-random cause.