5501.002&003 Assignment six 1.(10) The owner of the pizza chain wants to monitor the total weight of pepperoni. Suppose that for pizzas in this population, the weights have a mean of 250g and a standard deviation of 4g. Management takes a random sample of 64 of these pizzas and calculates the mean weight of the pepperoni on the pizzas. Assume that the pizzas in the sample are independent. What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251g? 2.(10) The Department of Tourism reported that in May of 2017, approximately 63%, percent of the 500,000 tourists to the Philippines were from Asia. Suppose another organization had taken a simple random sample of 600 of the tourists in that population, and assume that the reported 63% percent claim is accurate, what is the approximate probability that another organization's results were within 2 percentage points of the Department of Tourism's results? 3.(10) Suppose a simple random sample of 150 students is drawn from a population of 3000 college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the students' IQ score? 4.(10) Lily wants to estimate what proportion of computers produced at a factory have a certain defect. A random sample of 200 computers shows that 12 computers have the defect. She is willing to assume independence between computers in the sample. Based on this sample, what is a 95% confidence interval for the proportion of computers that have the defect? 5.(10) Sophia obtains a random sample of large coffees of two types and measures the amount of caffeine in each coffee. Here are summary statistics for her samples: Light roast Dark roast Sample mean x =170 mg x =164 mg Sample standard deviation s =5 mg s =3 mg Sample size n =52 n =72 Assume that the conditions for inference have been met, and that Sophia will use the conservative degrees of freedom from the smaller sample size. What is a 95% confidence interval for the difference in the mean caffeine content of a large coffee of the two types? 6.(10) A study suggests that about 80% of undergraduate students are working at a job. Researchers plan to do a new study and use the new data to make a z interval to estimate the proportion of students who are working at a job. They plan on using a confidence level of 90% and they want the margin of error to be no more than 1%. Let p represent the proportion of students who are working at a job and assume p = 0.80, what is the smallest sample size required to obtain the desired margin of error? 7.(25) For the data in the table: 1). Find the linear regression line, = + x 2). Find the estimate of the standard deviation of error, se 3). What is the standard error of the slope? 4). What is the t-statistic for testing the null hypothesis that the population slope in this setting is 0? y 29 32 13 17 4 x 60 28 32 30 0 8.(15) What is the 90% confidence interval for the slope of the least square regression line from above question? (use t-statistic)