1.Given the information below, enter the p-value to test the following hypothesis at the 1% significance level : Ho : 1 = 2 Ha : 1 2 Sample 1 Sample 2 n1 = 20 n1 = 20 x1 = 118 x1 = 113 s1 = 23.9 s1 = 21.6 What is the p-value for this test ? 2. Do top business executives tend to vote Republican? How large a sample n would you need to estimate the proportion of business executives who vote republican with margin of error 0.01 with 99% confidence? 3. A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile strength of 5.5 pounds per millimeter (lbs/mm). The company tests a random sample of 36 such valve plates from a lot of 200 valve plates (population size N=200). The sample mean is 5.613 lbs/mm, and the population standard deviation is 0.334 lbs/mm. The company wishes to use a significance level = .10 to conduct a hypothesis test to determine whether the lot of valve plates has an average tensile strength of 5.5 lbs/mm. What is the observed value of the test statistic z for the hypothesis test ? 4. An analyst from an energy research institute in Florida wants to estimate the average price of unleaded gasoline in the state. using a 95% confidence interval. He assumes the standard deviation estimate of $ 0.22 as reported in the popular press. How many gas stations should he include in his sample to be within $ 0.07 of the actual average gas price ? 5. Compute a 90% confidence interval to estimate the population proportion given a sample size of 1150 and a sample proportion of 25%. The interval estimate you found is : From 23.87% to 28.13% None of the Above From -0.05% to 0.10% From 22.90% to 27.10% 6. A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help and she informs them that the last 23 houses that sold in their neighborhood took an average time of 201 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 34 days. What is the margin of error of the 90% confidence interval for the mean sale time for all homes in the neighborhood ? (Use two decimal places) 7. A psychologist is studying learning rats. The psychologist wants to determine the average time required for rats to learn to traverse a maze. She randomly selects 10 rats and records the time it takes for the rats to traverse the maze in minutes. What is the point estimate of the population parameter (the mean amount of time required for the population of rats to learn to traverse a maze ? (Use 2 decimals for your answer) # time (minut es) 1 4.93 2 4.6 3 3.12 4 4.3 5 83 6 40 7 30 8 67 9 57 10 86 8. An agency that offers tutoring students for students taking the SAT is interested in evaluating the effectiveness of their programs. A random sample of 5 students is used to evaluate if their SAT score increases by more than 50 points after completing their program. The score of the 5 students before and after completing the program is shown below. Student 1 2 3 4 5 Score before the 400 520 700 600 425 training Score after the 450 600 735 660 460 training Using a significance level of 5%, What is the p-value of the Hypothesis test to determine if the training is effective in increasing the students score by more than 50 points ? (use 3 decimals) 9. A restaurant manager collects the data shown below on the number of customers served on 5 randomly selected weekdays. Week 1. 2. 3. 4 5 Number of Customers 38 15 11 17 22 Assuming the number of customers is normally distributed, compute the margin of error of a 90% confidence interval to estimate the average number of customers served by the restaurant on weekdays.________ (Use 3 decimals) 10. A report on the U.S. economy indicates that 25% of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 300 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 85 reported such difficulty. We want to use this data to determine whether the problem is more severe among these 10 cities. (i.e. the proportion of Americans experiencing difficulties making payments is significantly higher in these cities). a. What would be the correct conclusion at 5% significance level ? ( = 0.05) We conclude that there is evidence that the proportion of Americans experiencing difficulty making mortgage payments is significantly higher in these cities. b. A conclusion cannot be determined from the information given. c. We can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is equal to 25%. d. We conclude that there is NO evidence that the proportion of Americans experiencing difficulty making mortgage payments is significantly higher in these cities