Question

Provide an appropriate response. The commercial for the new Meat Man Barbecue claims that it takes 13 minutes for assembly with a population standard deviation of 2 minutes. A consumer advocate thinks that the assembly time is higher than 13 minutes. The advocate surveyed 10 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 13.7 minutes. Calculate the test statistic.

Answer 1

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).