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
is this one tailed or two tailed test
See most recent post.
To determine whether it is a t-test or z-test, we need to consider the information given. In this case, the sample size (n) is 64, which is relatively large. Generally, for large sample sizes (typically n > 30), we can use a z-test. However, since we do not have the population standard deviation (only the sample standard deviation), we will use a t-test.
Now, let's determine if this is a one-tailed or two-tailed test. The question states that we want to know if wages, on average, have gone up since the time when the average weekly earnings were $424. Since we are only interested in whether the average has increased (one direction), this is a one-tailed test.
To carry out the t-test, we will follow these steps:
1. Set up the hypotheses:
Null hypothesis (H0): The average salary is not significantly different from $424.
Alternative hypothesis (Ha): The average salary is significantly higher than $424.
2. Select the significance level (alpha): In this case, the level of significance is given as 0.05.
3. Calculate the test statistic:
To calculate the t-test statistic, use the formula:
t = (sample average - population mean) / (sample standard deviation / sqrt(n))
4. Determine the critical value:
Since this is a one-tailed test, we need to find the critical value associated with a significance level of 0.05 in the upper tail of the t-distribution table with degrees of freedom (df) = n - 1.
5. Compare the test statistic with the critical value:
If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
By following these steps, you can carry out the t-test and determine if there is a significant difference in the average salary.