The mean weight of all 20-year old women is 130 pounds. A random sample of 30 women athletes who are 20 years old showed a sample mean of 126 pounds with a standard deviation of 15 pounds. Researchers wanted to determine whether the mean weight for 20-year old women athletes is significantly less than 130, using a significance level of 0.05.
a. Write the null and alternate hypothesis.
b. Calculate the test statistic and write a conclusion for this question.
c. Now suppose a sample of 100 women athletes was taken and the same mean (126) and standard deviation (15) was achieved. Repeat the test.
d. Explain what caused the difference between the outcomes for parts b and c.