Question

Babies: A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of 4.3 pounds. Assume that the population of weights is normally distributed. A pediatrician claims that the standard deviation of the weights of one-year-old girls is less than 4 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the 0.01 level of significance.

Answer 1

The null and alternative hypothesis is ,

The test is one-tailed test.

Now , df=degrees of freedom=n-1=25-1=24

The critical value is ,

; The Excel function is , =CHIINV(0.99,24)

The test statistic is ,

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

Conclusion : There is not convincing evidence that the pediatrian's claim is true.

i.e. There is not sufficient evidence to support the pediatrician claims that the standard deviation of the weights of one-year-old girls is less than 4 pounds.