I am trying to understand this problem completely in order to be able to do the rest of my homework with similar problems.
Part 1 - Hypothesis Test About a Population Mean, when observed data is a "large" sample (n ≥ 30), and standard deviation is known
The manufacturer of the FireHouse tire claims that the mean mileage the tire can be driven before the tread wears out is at least 80,000 miles (mean ≥ 80,000), with a known population standard deviation of 6,400 miles. An off site company bought 100 of these tires randomly selected from the population of tires manufactured for its rental cars and found the sample mean mileage before the tread wore out to be 79,000 miles. Test the above claim by this manufacturer using a .03 significance level.
Part 2 - Hypothesis Test About a Population Mean, when observed data is a "small" sample (n < 30)
The manufacturer of the FireHouse tire claims that the mean mileage the tire can be driven before the tread wears out is more than 80,000 miles (Mean > 80,000). An off site company bought 49 of these tires randomly selected by the retail sales outlet from the production batch for its fleet of rental cars and found the sample mean mileage before the tread wore out to be 83,000 miles and with a sample standard deviation of 8,100 miles. Test the above claim by this manufacturer using a .05 significance level.
Any help would be great thanks!
Part 1 - Hypothesis Test About a Population Mean, when observed data is a "large" sample (n ≥ 30), and standard deviation is known
The manufacturer of the FireHouse tire claims that the mean mileage the tire can be driven before the tread wears out is at least 80,000 miles (mean ≥ 80,000), with a known population standard deviation of 6,400 miles. An off site company bought 100 of these tires randomly selected from the population of tires manufactured for its rental cars and found the sample mean mileage before the tread wore out to be 79,000 miles. Test the above claim by this manufacturer using a .03 significance level.
Part 2 - Hypothesis Test About a Population Mean, when observed data is a "small" sample (n < 30)
The manufacturer of the FireHouse tire claims that the mean mileage the tire can be driven before the tread wears out is more than 80,000 miles (Mean > 80,000). An off site company bought 49 of these tires randomly selected by the retail sales outlet from the production batch for its fleet of rental cars and found the sample mean mileage before the tread wore out to be 83,000 miles and with a sample standard deviation of 8,100 miles. Test the above claim by this manufacturer using a .05 significance level.
Any help would be great thanks!