• On questions requiring a numerical answer, show how the answer was obtained, by attaching Excel files, and a copy of your manual calculations on words Exercise 4-136 on page 227 State the null and the alternative hypotheses, and indicate the type of critical region (either two-tailed, lower-tailed, or upper-tailed) to test the following claims. (a) A manufacturer of lightbulbs has a new type of lightbulb that is advertised to have a mean burning lifetime in excess of 5000 hours. (b) A chemical engineering firm claims that its new material can be used to make automobile tires with a mean life of more than 60,000 miles. (c) The standard deviation of breaking strength of fiber used in making drapery material does not exceed 2 psi. (d) Skip (e) A biomedical device is claimed to have a mean time to failure greater than 42,000 hours. (f) Producers of 1-inch diameter plastic pipe claim that the standard deviation of the inside diameter is less than 0.02 inch. (g) Lightweight, handheld, laser range finders used by civil engineers are advertised to have a variance smaller than 0.05 square meters. Exercise 4-25(a) on page 169 A manufacturer is interested in the output voltage of power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 V, and the manufacturer wishes to test 𝐻0 : 𝜇 = 9 𝑉 against 𝐻1 : 𝜇 ≠ 9 𝑉, using n = 10 units. (a) The critical region is 𝑥̅ < 8.85 or 𝑥̅ > 9.15 Find the value of α. (b) Find the power of the test for detecting a true mean output voltage of 9.1 V. Exercise 4-27 on page 169 Consider exercise 4-25, and suppose that the process engineer wants the type I error probability for the test to be 𝛼 = 0.05. Where should the critical region be located? Exercise 4-31 on page 184 Consider the Minitab output shown below: One-Sample Z Test of 𝜇 = 30 vs 𝜇 ≠ 30 The assumed standard deviation = 1.2 N Mean SE Mean 16 31.2000 0.3000 95% CI (30.6120, 31.7880) Z P ? ? (Note: Standard Error of the Mean - We can see that the SE Mean is simply the standard deviation divided by the square root of the number of data points and represents the dispersion or variation in the distribution of sample means.) (a) Fill in the missing values in the output. What conclusions would you draw about rejecting or not rejecting the null hypothesis? (b) Is this a one-sided or a two-sided test? (c) Use the output and the normal table to find a 99% confidence interval on the mean. (d) What is the P-value if the alternative hypothesis is 𝐻1 : 𝜇 > 30? Exercise 4-36 on page 185 A random sample has been taken from a normal population and two confidence intervals constructed using exactly the same data. The two Cis are (38.02, 61.98) and (39.95, 60.05). (a) What is the value of the sample mean. (b) One of these intervals is a 90% CI and the other is a 95% CI. Which one is the 95% CI and why?
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