Suppose a mechanic claims that a machine filling bottles with saline solution is not equal to 153 ml, on average. Several of his coworkers do not believe him, so the mechanic decides to do a hypothesis test, at a 1% significance level, to persuade them. He fills 18 bottles, collects the proper data, and works through the testing procedure: H0: μ=153; Ha: μ≠153 x¯=156 σ=13 α=0.01 (significance level)
Suppose a mechanic claims that a machine filling bottles with saline solution is not equal to 153 ml, on average. Several of his coworkers do not believe him, so the mechanic decides to do a hypothesis test, at a 1% significance level, to persuade them. He fills 18 bottles, collects the proper data, and works through the testing procedure:
- H0: μ=153; Ha: μ≠153
- x¯=156
- σ=13
- α=0.01 (significance level)
- The test statistic is:
z0=x¯−μ0σn√=156−1531318√=0.98
The critical values are −z0.005=−2.58 and z0.005=2.58
Conclude whether to reject or not reject H0, and interpret the results.
-Reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis.
-Reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean filled bottle of saline solution is not equal to 153 ml.
-Do not reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis.
-Do not reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean filled bottle of saline solution is not equal to 153 ml.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
