Final answer:
The test statistic for the hypothesized mean assembly time of a Meat Man Barbecue, given a sample mean of 13.7 minutes, a population standard deviation of 2 minutes, and a sample size of 10, is approximately 1.11.
Step-by-step explanation:
The student is asking how to calculate the test statistic for a hypothesis test where the null hypothesis claims the mean assembly time for the Meat Man Barbecue is 13 minutes with a known population standard deviation. We are given a sample mean of 13.7 minutes, a population standard deviation of 2 minutes, and a sample size of 10. To calculate the test statistic, which is a z-score in this case, we can use the formula:
Z = (\bar{x} - \mu) / (\sigma/\sqrt{n})
Where:
- \(\bar{x}\) is the sample mean (13.7 minutes),
- \(\mu\) is the population mean (13 minutes),
- \(\sigma\) is the population standard deviation (2 minutes), and
- \(n\) is the sample size (10).
Plugging these values into the formula, we get:
Z = (13.7 - 13) / (2/\sqrt{10})
Z = 0.7 / (2/3.1623)
Z = 0.7 / 0.6325
Z = 1.1064
The test statistic is approximately 1.11 (rounded to two decimal places).