Final answer:
The power of a z test to detect a specified mean increase cannot be determined from the given information without the sample size and specific null hypothesis mean. Additional information is required to perform the calculation using standard statistical methods.
Step-by-step explanation:
The question asks to find the power of a z test to detect a mean increase of 2 seconds when the managers assume a significance level of α = 0.10 and a population standard deviation σ = 4. The power of the test is the probability of correctly rejecting the null hypothesis when a specific alternative hypothesis is true. In this case, we're interested in the power to detect a mean increase to μ = 102 seconds from the null hypothesis mean (μ0). The steps you provided for conducting a z-test on a calculator are indeed relevant for carrying out a hypothesis test, but they are specific to a different problem with its own dataset.
To calculate power, we would normally need to first calculate the z-score that corresponds to the significance level and then use the effect size (difference between μa and μ0) along with the standard deviation and sample size to find the power. This can be done using statistical software or power tables. Since we are not given the sample size (n), nor the specific mean under the null hypothesis (μ0), we cannot directly calculate the z-score or the power in this case.
Therefore, without additional information, we cannot determine which of the options (a) 0.10, (b) 0.20, (c) 0.80, or (d) 0.90 is the correct power of the z test. In practice, assuming that the sample size is sufficiently large, detecting a mean increase of 2 seconds with a standard deviation of 4 and at a significance level of 0.10, we might expect the power to be reasonably high (likely closer to options c or d). However, this is speculative without specific calculations.