Question: A construction company is interested in the thermal inertia properties of a brand of autoclaved aerated concrete used as building material. The company is looking to use the concrete to construct a building for a client. The client is requiring that the company use concrete with an average interior temperature of at least 22 degrees Celsius. They randomly sample 12 specimens of the brands concrete and calculate a sample mean of 22.22 degrees Celsius and a sample standard deviation of 0.275 degrees Celsius.

1. What hypothesis should the construction company test?
2. If the concrete used by the construction company doesn’t meet the clients specifications, the company has agreed to a 50% reduction in payment. They absolutely want to avoid this reduction so that the job is profitable. Based on this, would it make more sense to use a significance level of 0.01, or 0.05? Explain.
3. Using the significance level chosen in part b, perform the hypothesis test to determine whether the brand of concrete will meet the clients specifications. Specify the test statistic value, determine the p-value, and make a decision. You may assume the interior temp of the concrete follows a normal distribution.

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