The manufacturer of the X-15 steel-belted redial truck tire claims that the mean mileage the tire can be driven before the tread wears out is at least 60,000 miles.
Crosset Truck Company bought a sample of 48 tires and found that the mean
mileage for its trucks is 59,000 miles (i. e. less than the manufacturer’s claim) with
a standard deviation of 5,000 miles.
1) Test the manufacturer’s claim at a significance level (α) equals 5%.
2) Would your answer in part (1) change if the probability of type I error
equals zero? Justify your answer.

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3) Would your answer in (1) change if the confidence level changes to be
99%. Justify your answer with proper test.
4) Another engineer has argued that tiers are considered to be fully
consumed after 120000 mileage, test this claim at significance level of
10%.
5) If the manager of a store is thinking about establishing a new billing
system for the store's credit costumers. After a thorough financial analysis,
she determines that the new system will be cost effective only if the mean
monthly income is more than 170£. A random sample of 400 monthly
accounts is drawn, for which the sample mean is 178£. The manager
knows that the accounts are normally distributed with standard deviation
of 65£. Can the manager conclude from this that the new system will be
cost-effective at significance level (α) equals 5%.?