Question

Let's say that you're in charge of a survey asking about the true population mean of the weight of american adults between the ages of 18 and 30. The magazine "american journal of medicine" claims that the population mean weight is 195 for Americans between the ages of 18 and 30. You know nothing of the population parameters. You take an SRS of 300 adults between the ages of 18 and 30 and find a sample mean of 180 with a sample standard deviation of 18 (both in pounds). Use a level of significance of .05 to test the "American journal of medicines" claim. Please explain your conclusions.

Answer 1

Hypothesis:

Test statistic,

Degrees of freedom = n-1 = 300 - 1 = 299

Critical value = 1.97 at 5% level of significance.

Here we see that absolute value of test statistic is greater than critical value, hence we reject null hypothesis and conclude that  mean weight of Americans between the ages of 18 and 30 is not equal to 195 pounds.

Hence "American journal of medicines" claim is not true.