A tire manufacturer claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000 miles. A survey of owners of that tire design is conducted. From the 44 tires surveyed, the mean lifespan was 48,500 miles with a standard deviation of 8,800 miles. We want to determine if this information is inconsistent with the manufacturer's claim, using significance level = 0.05. Suppose that mu is the true mean lifespan of all deluxe tires from this manufacturer.

Question 1: What are the null and alternative hypotheses that should be tested?

Question 2: What is the standardized value of the test statistic?

Question 3: Complete this sentence: At significance level 0.05, we reject H0 if ________.

Question 4: Do we reject the null hypothesis?

Question 5: Based on this hypothesis test, can we conclude that the mean lifespan is less than 50,000 miles?

Question 6: Should the p-value for this test be greater than or less than the significance level?

Question 7: Calculate the p-value for this test