the average weekly earnings of a production worker were $424. to know if wages, on average, have gone up since that time. To test this, you sample 64 production workers, and determine that their average salary is $432.69, with a sample standard deviation of $33.90. Use a 0.05 level of significance .carry out test .

Question

is it t test or z test ? how would we know
in this case is this one tailed or two tailed how can we conclude

Answer 1

Usually you use z-tests when sample sizes are large (n is greater than
or equal to 30) whether or not you know the population standard deviation.

If you do not know the population standard deviation and have a small
sample (n < 30), then you can use t-tests.

You can determine the direction of the test by reading the problem. The problem says "gone up" which can be interpreted to mean "greater than" in your alternate hypothesis. If your alternate hypothesis shows a specific direction (like "greater than" or "less than"), then the test will be one-tailed. If you use "does not equal" in the alternate hypothesis (the results can be in either direction), then the test is two-tailed.

I hope this will help get you started.

Answer 2

i thought its a t test as it says sample standard deviation.
the main problem i get here is how to write null and alternative hypotheses as i cant decide whether it is one tailed or two tailed test.

Answer 3

Ho: µ = $424 --->null hypothesis
Ha: µ > $424 --->alternative hypothesis

Since the alternative is showing a specific direction, the test is one-tailed.

Answer 4

thank you