Question

In: Statistics and Probability

A study reported in the Journal of the American Medical Association involved the study of respiratory...

  1. A study reported in the Journal of the American Medical Association involved the study of respiratory tract infections in children aged 1 to 5 years in Israel. During the period November 1999 to March 2000 a randomly selected group of the children received a placebo and another randomly selected group received a mixture of Echinacea and Vitamin C. The following table gives the numbers for the children in each group and for those who developed pneumonia during that time.

Treatment:

Sample Size

Number who developed pneumonia

Placebo

168

38

Echinacea and Vitmin C

160

13

Total:

328

51
  1. Calculate the sample proportion, , of children in the placebo group who developed pneumonia, and calculate the sample proportion, , of children in the Echinacea group who developed pneumonia.
  1. Calculate the sample difference in proportions, .
  1. Calculate the approximate standard error, s, of the sampling distribution for differences in sample proportions.

d. Calculate a 95% confidence interval for the difference in the population proportions, .

  1. Interpret, in terms a non-statistics person would understand, your 95% confidence interval, explaining what it tells us about the proportions of all children with these treatments who would develop pneumonia.
  1. State an appropriate null hypothesis, H0, and alternative hypothesis, H1, for testing whether or not the proportion of children developing pneumonia is higher for the placebo treatment than for the Echinacea treatment.

H0: English version:

Symbolic version:

H1: English version:

Symbolic version:

  1. Calculate the pooled proportion, , and the standard error, s, based on the pooled proportion. (Hint: the last row in the table gives you pooled numbers.)
  1. Calculate the z-score for your sample difference, , from part b.
  1. Calculate the p-value for your z-score. If the significance level is 0.01, should the researchers reject or fail to reject the null hypothesis from part f?
  1. Explain your conclusion from the previous part in terms a non-statistics person would understand.

Solutions

Expert Solution

orchestra answered 1 year ago
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