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 .
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
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.
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.
Ho: µ = $424 --->null hypothesis
Ha: µ > $424 --->alternative hypothesis
Since the alternative is showing a specific direction, the test is one-tailed.
thank you
To determine whether to use a t-test or a z-test, we need to consider the sample size and whether we know the population standard deviation.
In this case, you have a sample size of 64 production workers. If the population standard deviation is known, then you can use a z-test. However, since the problem states that you have a sample standard deviation, we will use a t-test.
Now, let's determine whether this is a one-tailed or two-tailed test. A one-tailed test is used when we have a specific direction for the hypothesis (e.g., testing whether the wages have increased), while a two-tailed test is used when we do not have a specific direction (e.g., testing whether the wages have changed).
In this case, the question states that we want to know if wages, on average, have gone up since the average weekly earnings of $424. Therefore, we have a specific direction and we will use a one-tailed test.
To carry out the test, we need to perform the following steps:
1. Set up the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis assumes no change in the wages, and the alternative hypothesis assumes that the wages have increased.
2. Calculate the test statistic. For a t-test, the formula is:
t = (sample_mean - population_mean) / (sample_standard_deviation / sqrt(sample_size))
3. Determine the critical value. This is based on the significance level (0.05) and the degrees of freedom (sample_size - 1 = 63) for a one-tailed test.
4. Compare the test statistic to the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the wages have increased. If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that the wages have increased.
By following these steps, you can carry out the test and make your conclusion.