The manager of a paint supply store wants to determine whether the

  1. The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer actually is 1 gallon. It is known from the manufacturer’s specifications that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the mean of the amount of paint per 1-gallon can is found to be .995 gallon.a. Is there evidence that the mean amount is different from 1.0 gallon (use a=0.01)?b. Compare the p-value and interpret its meaning.c. Construct a 99% confidence interval estimate of the population mean amount of paint.d. Compare the results of (a) and (c). What conclusions do you reach?2. If you use a 0.05 level of significance in a two tail hypothesis test, what will decide if zstat = -0.76?3. The quality- control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.a. At the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?b. Compute the p- value and interpret its meaning.c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.d. Compare the results of ( a) and ( c). What conclusions do you reach?