Question

We would like to test at a level of significance ? = 0.05 whether the population mean is less than 120. A random sample of size 49 is taken with a mean of 122. Assume ? = 4 and normally distributed population. Find the Zdata and round it to two decimal places.

Answer 1

To test against

Here

sample mean

population standard deviation

and sample size n = 49

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of signficance if

Now,

The value of the test statistic (ans)

and critical value

Since , so we fail to reject H₀ at 5% level of signficance and we can conclude that the population mean is not significantly less than 120.