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Two types of medication for hives are being tested to determine if there is a difference...

Two types of medication for hives are being tested to determine if there is a difference in the proportions of adult patient reactions. Twenty out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. Twelve out of another random sample of 180 adults given medication B still had hives 30 minutes after taking the medication. Test at a 1% level of significance.

1. The null and alternative hypothesis would be:

  • A. H0:μA=μB

    H1:μA<μB

  • B. H0:pA=pB

    H1:pA<pB

  • C. H0:μA=μB

    H1:μA≠μB

  • D. H0:pA=pB

    H1:pA≠pB

  • E. H0:μA=μB

    H1:μA>μB

  • F. H0:pA=pB

    H1:pA>pB

2. State the null and alternative hypothesis as a difference statement?

  • A. H0: pA - pB = 0

    H1:pA - pB > 0

  • B. H0: μA - μB = 0

    H1:μA - μB > 0

  • C. H0: pA - pB = 0

    H1:pA-pB≠ 0

  • D. H0: μA - μB = 0

    H1:μA - μB≠0

  • E. H0: pA - pB = 0

    H1:pA - pB < 0

  • F. H0: μA - μB = 0

    H1:μA - μB < 0

3. Now we are going to investigate the effect that sample size has on a hypothesis test. We will keep the point estimator (ie. the fraction will remain the same) the same but change the sample size.

What would be your p-value if the sample size for both sets doubled (Sample for Medicine A was out of 400 people, Sample for Medicine B was out of 360 people)? (Hint: to keep the point estimate the same, if you double the denominator, you must also double the numerator).

Rerun the hypothesis test and find the p-value.

p-value =

(Round to the 3rd decimal place)

What would be your p-value if the sample size for both sets tripled (Sample for Medicine A was out of 600 people, Sample for Medicine B was out of 540 people)? (Hint: to keep the point estimate the same, if you double the denominator, you must also double the numerator).

Rerun the hypothesis test and find the p-value.

p-value =

(Round to the 3rd decimal place)

What would be your p-value if the sample size for both sets quadrupled (Sample for Medicine A was out of 800 people, Sample for Medicine B was out of 720 people)?

p-value =

(Round to the 3rd decimal place)

4. What happens to the p-value as we increase the sample size?

5. Estimate the needed sample size for both Medication A and Medication B needed at these point estimators to reject the null hypothesis at a 0.01 significance level.

math   Statistics-And-Probability   
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