Question

In: Statistics and Probability

Type I vs. Type II error; Alpha vs. beta risk; Alpha level, p-value; How to calculate...

  • Type I vs. Type II error; Alpha vs. beta risk; Alpha level, p-value;
  • How to calculate a confidence interval and what it actually represents (e.g. what are you confident about?);
  • Experimental designs;
  • How to determine degrees of freedom and calculate a standard error of the mean;
  • When to use and how to calculate 1-sample, two sample and paired t-tests; Mann-Whitney-U and Wilcoxon Matched-pairs Sign Rank tests;
  • Types of variables and their scales of measurement;
  • Attributes of a scientific hypothesis;
  • Kurtosis and skewness;
  • Assumptions of the t-test.

Statistical hypotheses. State the appropriate (1) statistical test, (2) experimental design (where appropriate) and (3) statistical null hypothesis for the following (set a=0.05 and assume normality unless otherwise stated).

1. Research question: Is the mean amount of exposure to microwave radiation less than 10 microwatts/cm2?

Test:

Ho:                                                                          H1:

2. Research question: Is the mean amount of exposure to microwave radiation differ from the DOE specified exposure threshold of 15 mw/cm2 ?

Ho:                                                                          H1:

3. Blood CO2 tension (mm Hg) was measured in patients with chronic hypercapnic respiratory failure before and after a weight loss program. Research question: Does the weight loss program affect CO2 tension?

Experimental design:                                                                          Test:

Ho:                                                                          H1:

4. Urinary excretion of 5-HIAA (mg/24 hrs) was compared in two groups of individuals: those with carcinoid heart disease and those without disease. You suspect that that the distribution of at least one sample is not normally distributed. Research question: Does 5-HIAA excretion differ between the groups?

Test:

Ho:                                                                          H1:

5. Blood temperature of the brachial artery is measured as it enters the flipper of a porpoise and again as it exits the flipper in the brachial vein. Twenty-four total blood temperature readings were obtained from twelve porpoises. Research question: Does arterial blood temp. greater than that of venous blood temperature?

Experimental design:                                                                                          Test:

Ho:                                                                          H1:

6. Perceived exertion levels are ranked for a group of couch potatoes while resting and then again after running on a treadmill. Research question: Does perceived exertion differ between the before and after measurements?

Experimental design:                                                                                          Test:

Ho:                                                                          H1:

7. To determine the effectiveness of a new blood pressure drug, 10 individuals receive the drug and 10 people get a placebo. Individuals of similar age and hypertension were assigned one to each treatment. Does the new drug have an effect?

Experimental design:                                                                                          Test:

Ho:                                                                          H1:

8. Beagles with chronic hyperactivity were randomly placed into two groups; one group received Coma-calm (doggie Prozac) and the other group a placebo. Activity levels of the two groups were ranked 2-hours after administration. Research question: Is Coma-calm effective in reducing hyperactivity levels?

Scale of measurement:                                                                                       Test:

Ho:                                                                          H1:

9. For the following hypotheses and sample sizes, determine the critical value with which the test statistic is compared:

  1. Ho: μ = 40, n = 32, a=.05                                  tcrit:____________________

  1. Ho: μa > μb, n = 22, a=.01                                tcrit:____________________                            

  1. Ho: D = 36.5, n = 12, a=.05                          tcrit:____________________

Solutions

Expert Solution

(1)

H0: Mean amount of exposure to microwave radiation greater than and equal to 10 microwatts/cm2

H1: Mean amount of exposure to microwave radiation less than 10 microwatts/cm2

(2)

Is the mean amount of exposure to microwave radiation differ from the DOE specified exposure threshold of 15 mw/cm2 ?

H0: Mean amount of exposure to microwave radiation does not differ from the DOE specified exposure threshold of 15 mw/cm2

H1: Mean amount of exposure to microwave radiation differ from the DOE specified exposure threshold of 15 mw/cm2

(3)

H0:   The weight loss program does not affect CO2 tension

H1: The weight loss program affect CO2 tension

(4)

H0:   5-HIAA excretion doesn't differ between the groups

H1:   5-HIAA excretion differ between the groups

(5)

H0:   Arterial blood temp. smaller than and equal to that of venous blood temperature

H1: Arterial blood temp. greater than that of venous blood temperature

(6)

H0:   perceived exertion doesn't differ between the before and after measurements

H1:   perceived exertion differ between the before and after measurements

(7)

H0:   the new drug doesn't have an effect

H1:   the new drug have an effect

(8)

H0:   Coma-calm effective in not reducing hyperactivity levels

H1:   Coma-calm effective in reducing hyperactivity levels


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