The effectiveness of a headache medicine is tested by

Question

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 construct a 99%confidence interval for µ₁ - µ₂ where µ₁ and µ₂ represent the mean for the treatment group andthe control group respectively.Show all steps of the hypothesis test and all calculations. Use the following t-distribution table - https://www.itl.nist.gov/div898/handbook/eda/section3/eda3672.htm

Treatment Group                            Control Group

n₁ = 85                                                  n₂ = 75

x₁^- = 189.1                                           x₂^- = 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.

Student	A	B	C	D	E
Before	71	66	67	77	75
After	75	75	65	80	87

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,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.

Answer 1

Answer the following statistics problem, by providing the complete procedural part. Q1. Find out whether the samples are independent or dependent. The efficiency of a new headache medicine is tested via measuring the amount of time before the headache is healed for patients who make use of the medicine and the other group of patients who make use of a place drug. Describe. Q2. Find out whether the samples are independent or dependent. The efficiency of a headache medicine is tested via measuring the intensity of headache inpatients before and after the drug treatment. The data comprise of before and after intensities for each patient. Describe. Q3. In an arbitrary sample of 500 people aged 20 to 24, 22% were smokers. In an arbitrary sample of 450 people aged 25 to 29, 14% were smokers. Test the claim which the proportion of smokers in the two age groups is similar. Make use of a significance level of 0.01.Illustrate all the steps of hypothesis test and all computations.