1. If the margin of error in an estimate for the mean weight of a shipment is + or -2 pounds at a confidence level of 95 percent, what will be the margin of error at a confidence level of 98 percent? Be sure to show how you arrived at your answer.
2. Describe in detail how you would construct a 95% confidence interval for a set of 30 data points whose mean is 20 and population standard deviation is 3. Be sure to show that you know the formula and how to plug into it.
Also, clearly state the margin of error.
3. Generally speaking, what is the conclusion if p is less than 5%?
4. Generally speaking, what is the conclusion if p is greater than 5%?
5. Each of the following situations requires a significance test about a population mean µ. State the appropriate null hypothesisand alternative hypothesis in each case.
a) The mean area of the several thousand apartments in a new development is advertised to be 1250 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion.
b) Larry's car averages 32 miles per gallon on the highway. He switches to a new motor oil that is advertised as increasing gas mileage. After driving 3000 highway miles with the new oil, he wants to determine if his gas mileage actually has increased.
c) The diameter of a spindle in a small motor is supposed to be 5 millimeters. If the spindle is either too small or too large, the motor will not perform properly. The manufacturer measures the diameter in a sample of motors to determine whether the mean diameter has moved away from the target.
6. A test of the null hypothesis H0: µ = 0 gives test statistic z = 1.8.
a) What is the P-value if the alternative is Ha: µ > µ0?
b) What is the P-value if the alternative is Ha: µ < µ0?
c) What is the P-value if the alternative is Ha: µ ≠ µ0?