Homework 4

Biostatistics 6030-70

Note: The homework is worth one extra credit point towards the final grade.

Dataset 1(Questions 1 to 7 are based on this dataset)

  1. In a study of nutritional requirements of cattle, researchers measured the weight gains of cows during a 78-day period. For two breeds of cows, Hereford (HH) and Brown Swiss/Hereford (SH), the results are summarized in the following table.

HH SH

Sample size 29 33

Sample mean 18.3 13.9

Sample variance 17.8 19.1

Did the Hereford (HH) cows gain more weight than the Brown Swiss/Hereford (SH)? Assume that the variances of the two populations of cows are equal. Set a at 0.10

  1. What is the null hypothesis?
  1. What is the alternative hypothesis?
  1. What is the test statistic used?

(b)*

  1. What is the calculated test statistic

  1. What is the critical value of the test statistic
  1. What is the p-value
  1. What is the statistical decision

Reject the null hypothesis. There is a significant difference in weight gained between the two group of cattle.

Dataset 2: Questions 8 –14 are based on this dataset.

Can we conclude that chronically ill children tend on the average, to be less self-confident than healthy children? A test designed to measure self-confidence was administered to 16 chronically ill and 21 healthy children. The mean scores and variances are as follows.

Let a =0.05. Assume that population variances are unequal

  1. What is the null hypothesis?
  1. What is the alternative hypothesis?
  1. What is the test statistic used?

(b)

  1. What is the calculated test statistic
  1. What is the critical value of the test statistic

  1. What is the p-value
  1. What is the statistical decision

Reject the null hypothesis. Average self-confidence is significantly different for the two populations

Dataset 3(Questions 15 to 21 are based on this dataset)

A test designed to measure level of anxiety was administered to a sample of male and a sample of female patients just prior to undergoing the same surgical procedure. The sample sizes and the standard deviation computed from the scores were as follows:

Do these data provide sufficient evidence to indicate that in the represented populations the scores made by females are more variable than those made by males? Let a =0.05

  1. What is the null hypothesis?
  1. What is the alternative hypothesis?

(a) 

  1. What is the test statistic used?
  1. What is the calculated test statistic
  1. What is the critical value of the test statistic
  1. What is the p-value
  1. What is the statistical decision

Retain the null hypothesis. Variability in female scores is not significantly different than variability in male scores