What is the Ho and Ha? What is the test statistic (t*)?

Question

A simple random sample of 15-year old boys from one city is obtained and their weights (in pounds) were collected. The sample average of the 11 boys was 154 pounds, with a sample standard deviation 18. Use a 0.01 significance level to test the claim that kids nowadays are getting smaller and smaller. According to the old data, the population of boys this age weigh on average 149 pounds.

Answer 1

One sample was taken so this is a one sample mean t-test.

The population mean is 149 and we want to see if boys are getting smaller.

Ho: population mean = 149

Ha: population mean < 149 (testing getting smaller, which is a left-tail test)

The sample size is 11, so the degrees of freedom will be 10 and for alpha = 0.01 we will use the 0.01 left tail value for 10 DOF = -2.764 for the critical t value.

The t-statistic = (sample mean - population mean) / standard deviation/sqrt(sample size), where sample mean = 154 and standard deviation is 18.

Since the sample mean is larger than the population mean, there really is no need to go through the left tail test as Ho will not be rejected unless the sample mean was less than the population mean.