Question

The average American eats 1.5 cups of vegetables a day (may not be accurate). A researcher is interested in whether teenagers eat less vegetables on average than does the average American. She takes a sample of 25 teenagers and asks how much vegetables they eat. She finds that the mean amount of vegetables her subjects eat a day is 1.1 cups with a standard deviation of 0.5. What would be the appropriate test for the researcher to use to test whether teenagers actually do eat less vegetables than the average American at an alpha level of .01?

Answer 1

Solution:

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 1.5

Ha: 1.5

The test statistics,

t =( - )/ (s /n)

= ( 1.1 - 1.5 ) / ( 0.5 / 25 )

= -4

P-value = 0.0003

The p-value is p = 0.0003 < 0.01, it is concluded that the null hypothesis is rejected.

There is sufficient evidence to test whether teenagers actually do eat less vegetables than the average American at an alpha level of .01.