Assignment Task:

Hypothesis Testing Method for Pipe Diameter Standards

Instructions:

Review each problem, understand the given data, and identify the question being asked. Determine the type of hypothesis test required to solve the problem. Follow the key steps for each hypothesis test, using the provided data.

Problem 1: You are an exobiologist and are a critical part of the SpaceX mission to Mars. Mr. Elon Musk himself bets you $1 million that these alien plants are on average shorter than 500 m.

Problem 2: A pipe manufacturer makes tubes with a diameter (in) of around 7.5 inches. The Quality Control (QC) specialist requires the tubes to have an average diameter of 7.5 inches. Will your samples pass the QC standard?

Problem 3: As a track and field coach, you`re seeking elite marathon runners. You`ve collected run times (in mins) for 10 runners over the last 20 runs each. Is there a statistically significant difference between the runners?

Problem 4: You decide to take 30 random samples from your performance-enhancing drug levels. Using a significance level of 0.050, determine if there is any indication of drug usage.

Problem 5: The marketing department ran a customer satisfaction survey, with scores ranging from 1 to 10. The ideal average score is 6 with a standard deviation of 1. Determine if the feedback score from the survey meets this expectation.

Problem 6: In engineering, the Brinell hardness score indicates the hardness of materials. An engineer measures the Brinell hardness of 25 pieces. Determine if there is a statistically significant difference in hardness.

Follow the steps for each hypothesis test, fill in the required tables, and analyze the results to draw appropriate conclusions.