The article “Limited Yield Estimation for Visual Defect Sources” (IEEE Trans. on Semiconductor Manuf., 1997: 17–23) reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 201 of these passed the probe. a) Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. b) perform the corresponding two-tailed hypothesis test

a) A simple random sample of thirty-six students has a mean age equal to x = 28.50 years, determine a 95% confidence interval estimate for u given o = 6.24 years. Give your answers to two decimal places. Determine the sample size needed for a maximum margin of error of two years for the 95% confidence interval estimate for μ given o = 6.24 b)

The impact energy is an important standard in metallic materials. Ten measurements of impact energy (J) on a steel sample are observed: 64.1, 64.7, 64.5, 64.6, 64.5, 64.3, 64.6, 64.8, 64.2 and 64.3. a) Find the 95% two-sided confidence interval for u. b) Determine the sample size if we would like to bound the length of the 95% two- sided confidence interval of u within 0.15 J (assume the sample standard deviation remains the same as of the ten measurements).

A job candidate at a large job fair can be classified as unacceptable, provisional, or acceptable. Based on past experience, a high-quality candidate is expected to get 80 percent acceptable ratings, 15 percent provisional ratings, and 5 percent unacceptable ratings. A high-quality candidate was evaluated by 100 companies and received 60 acceptable, 25 provisional, and 15 unacceptable ratings. A chi-square goodness-of-fit-test was conducted to investigate whether the evaluation of the candidate is consistent with past experience. What is the value of the chi-square test statistic and number of degrees of freedom for the test? x² (15–5)° (25–15) (60–80)² with 2df || 15 80 (15–5) (25–15) (60–80)? B with 3df 5 15 80 (15–5)² (25–15) (60–80)² with 99df 15 80 x² (5–15) (15–25) (80–60)² D with 2df 15 25 60 (5–15) (15–25)² (80–60)? E x² with 3df 15 25 60 ||

Traffic accidents occur frequently on the 100 km long E-5 highway connecting Konya and Karaman: Although expert teams affiliated to the General Directorate of Highways (KGM) say that the accidents on the E-5 are randomly (unevenly) distributed, the news media state the opposite. KGM has published the locations of 20 accidents resulting in death or injury in the past 12 months, showing the distances from Konya as follows: Use the Kolmogorov-Smirnov test to test whether the distribution of locations of accidents that occurred in the last 12 months is evenly distributed.

Exercise 1: You are interested in determining the average number of social media accounts people have. You interview 30 people at random and the number of social media accounts they have has a sample mean of 7.1 and a sample standard deviation of 2.09. a) b) Define the parameter of interest. State and check if the assumptions needed for constructing the appropriate CI for the parameter of interest are satisfied. c) Find a 90% confidence interval for the parameter defined in part a). Use the table, not the calculator to find the appropriate critical value. d) Write a sentence to interpret the CI computed in part c).

A taxi company is trying to decide: whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 12 of each brand. The tires are run until they wear out. The results are Brand A: = 36300 km ; sa = 5000 km Brand B: īR = 38100 km ; SR = 6100 km a) Compute a 95% confidence interval for Ha – HB assuming the populations to be approximately normally distributed and variances are inequal. b) Find a 99% confidence interval for µa – µB if a tire from each company is assigned at random to the rear wheels of 8 taxis and the following distance, in kilometers, recorded: Тaxi Brand A Brand B 1 34400 36700 2 45500 46800 3 36700 37700 32000 31100 5 48400 47800 32800 36400 7 38100 38900 8 30100 31500 Assume that the differences of the distances are approximately normally distributed.