Suppose that 500 parts are tested in manufacturing and 10 are rejected. Test the hypothesis Ho: p = 0.03 against H : p < 0.03 at a = 0.010. Find the P-value. The P-value is i Ho. . Round your answer to three decimal places (e.g. 98.765). The advertised claim for batteries for cell phones is set at 48 operating hours, with proper charging procedures. A study of 5000 batteries is carried out and 15 stop operating prior to 48 hours. Do these experimental results support the claim that less than 0.2 percent of the company's batteries will fail during the advertised time period, with proper charging procedures? Use a hypothesis- testing procedure with a = 0.08. The proportion of cell phone batteries that fail less than 0.2% at a = 0.08. The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 90, and the standard deviation is 2. You wish to test Ho: = 90 versus H 90 with a sample n=4 specimens. (a) If the acceptance region is defined as 88.5 91.5, find the type I error probability a. Round your answer to three decimal places (e.g. 98.765). i (b) Find for the case in which the true mean heat evolved is 93. Round your answer to three decimal places (e.g. 98.765). (c) Find for the case where the true mean heat evolved is 95. Round your answer to five decimal places (e.g. 98.76543). = i Compare this value of with the one found in part (b). Explain the difference if it exists. It is bigger because it is not likely to accept the product when the true mean is as high as 93. It is smaller because it is not likely to accept the product when the true mean is as high as 95. It is bigger because it is not likely to accept the product when the true mean is as high as 95. It is smaller because it is not likely to accept the product when the true mean is as high as 93. This value of is the same with the one found in part (b), because the true means are approximately equal. O This value of is the same with the one found in part (b), because the true means are approximately equal and other parameters do not change. A group of 15 students has performed an experiment, they measured the coefficient of thermal expansion for aluminum. The results are as follows (10-6K-). 22.0 25.0 25.6 22.2 22.7 24.9 24.9 20.8 26.1 23.7 23.5 20.1 21.4 22.8 20.4 At what level of significance do the students fail to reject the hypothesis that the mean coefficient value is the same as the table value of 22.2 x 10-6 K-? 0.8 0.1 O 0.2 O 0.5 Consider the hypothesis test of Ho: 02 = 7 against H:0 7. Approximate the P-value for each of the following test statistics. (a) x = 25.2 and n = 20. O 0.05 P-value < 0.10 O 0.1 (c) x = 23.0 and n = 15. O 0.05 P-value < 0.10 O 0.2 P-value < 1 O 0.1 P-value < 0.5 O 0.1 < P-value < 0.2