Inferences from Two Samples

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Module 4 Homework Assignment

1. Determine whether the samples are independent or dependent.

The effectiveness of a new headache medicine is tested by measuring the amount of time beforethe headache is cured for patients who use the medicine and another group of patients who use aplacebo drug. Explain.

2. Determine whether the samples are independent or dependent.

The effectiveness of a headache medicine is tested by measuring the intensity of a headache inpatients before and after drug treatment. The data consist of before and after intensities for eachpatient.Explain.

3. In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450people aged 25-29, 14% were smokers. Test the claim that the proportion of smokers in the twoage groups is the same. Use a significance level of 0.01.Show all steps of the hypothesis test and all calculations.

4. A researcher wishes to determine whether people with high blood pressure can reduce theirblood pressure by following a particular diet. Use the sample data below to perform all steps for hypothesis testing or construct a 99%confidence interval for µ₁ – µ₂ where µ₁ and µ₂ represent the mean for the treatment group andthe control group respectively. Use the following t-distribution table –

Treatment Group                            Control Group

n₁ = 85                                                  n₂ = 75

189.1                                            = 203.7

s₁ = 38.7                                               s₂ = 39.2

For questions 5 – 9 below, use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.

Five students took a math test before and after tutoring. Their scores were as follows.

Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.

5. State the null and alternative hypotheses.

6. Find d, , and s_d,

7. Find the value of the test statistic, t.

8. Find the critical value(s) and state the decision about the null hypothesis.

9. State the conclusion in non-technical terms.

Last Updated on March 4, 2018