scenario A

Au gr du vent specializes in the manufacture of windsurf boards. According to the owner, the average time to manufacture a sail is at most 16.8 hours. The data collected from a random sample of 100 boards allow us to determine an average manufacturing time of 17.2 hours with a standard deviation of 1 hour. We will hypothesis test the owner's claim.

issue 1 Formulate the null hypothesis and the counter-hypothesis.

issue 2 When performing a hypothesis test, it is important to identify a level of significance from the outset. Comment on this threshold and identify a possible consequence in the context of the problem.

issue 3 What are the conditions for applying the test?

question 4 What is the correct statistic for the test?

issue 5 With a 5% significance level, what is the decision rule?

issue 6 Calculate the reduced gap.

issue 7 Is the owner's claim accurate? Explain.

Scenario B

The sails are attached to the mast using previously cut ropes. These should be an average length of 30 cm with a standard deviation of 1 cm. A random sample of 36 strings is occasionally taken from production and the length of each string in the sample is measured. If the average length of the sample is less than 29.75 cm or greater than 30.25 cm, the cutting of the ropes is stopped until an employee adjusts the cutting equipment. If the average string length is within the range, everything is considered to be working normally and the cuts continue.

Question 8 What do you call the risk of stopping rope cutting unnecessarily when the equipment is well calibrated?

Question 9 Calculate the risk of stopping rope cutting unnecessarily when the equipment is well calibrated.

Question 10 What do you call the risk of not stopping rope cutting when the equipment is not properly calibrated?

Question 11 Calculate the risk of not stopping the equipment while it is calibrated at 30.15 cm.

Question 12 Calculate the power of the test when the equipment is calibrated at 30.15 cm.

Scenario C

For fun, the warehouse workers decided to hold a speed contest. They split into two groups (group A and group B) and timed how long it took to fold and pack the sails into their carry bag. Here are the results obtained: - Group A Group B Number of veil fold 52 56 Average time (in seconds) 172 168 Standard deviation 10 12

Question 13 Can we conclude, at the 5% level of significance, that group B is faster than group A?

Question 14 Can we conclude, at the 5% significance level, that the variance of the two groups does not differ significantly?

Scenario D The company uses high performance equipment to manufacture its sails. The owner noted the time required (in minutes) to complete the production of the sails (in square meters). Here is the data he collected: Production (in square meters) y Production time (in minutes) x 125 150 150 215 85 105 225 280 120 160 180 220 215,300 105 151 94 130

Question 15 What can be said about the form of the statistical link that may exist between these two variables?

Question 16 Calculate the coefficients b1 and b0 of the regression line.

Question 17 Give an estimate of the production (in square meters) corresponds to a production time of 150 minutes?

Question 18 What is the difference between the estimated value (question 17) and the observed value (see table) called? Why do we observe this discrepancy?