show all steps and do not just give the final answers. Material is based on Chapter 8 and 9 from Ahn. Please upload your homework to Blackboard and you have two attempts to upload correctly for each homework. 1. A toxicologist wishes to investigate the relationship between the probability of a developmental defect and the level of a certain acid in the environment. Twenty mg/kg/day of the acid is given to mice during pregnancy, and the malformation rate of the fetuses is observed. a) How large a sample should be chosen to estimate the proportion with 95% error margin of 0.01? Use p = .2. b) A random sample of 400 mice is taken, and 37 mice were found to have malformed fetuses. Construct a 95% confidence interval for the population proportion. 2. A random sample of size 13 from a normal population is given below. 69 85 74 86 75 87 76 80 78 79 81 83 83 a) Someone claimed that = 10. Does this data set support the claim? Test at = 0.05. b) Test if the population mean is 85 using = 0.05. c) Find the p-value of the test. 3. A test is conducted to compare the tread wear of certain type of tires on highways paved with asphalt and highways paved with concrete. Road tests were conducted with the same type of tires on two types of highways. Summary data on the mileage of the tires up to a certain level of wear are given below. Asphalt Concrete Sample Size 35 35 Sample Mean 29,700 25,500 Sample Standard Dev. 9,700 7,800 Does this information suggest that tires wear faster on concrete-paved highways than asphalt paved highways? Test using = 0.01. 4. In a study on the healing process of bone fractures, researchers observed the time required to completely heal a bone fracture. Ten rats were randomly divided into two groups of five. No treatment was done to one group and a medical treatment was given to the other group. The time spent (in days) to completely heal the fracture for each rat is given below: Control: 30, 22, 28, 35, 45 Treatment: 33, 40, 24, 25, 24 a) Test to see if the mean duration of healing can be reduced by the medical treatment at = 0.01. b) Construct a 99% confidence interval for the difference of the means of the two groups. 5. The following table shows summary data on mercury concentration in salmons (in ppm) from two different areas of the Pacific Ocean. Area 1: m = 15, Area 2: n = 15, x = 0.0860, s1 = 0.0032 y = 0.0884, s1 = 0.0028 Do the data suggest that the mercury concentration is higher in salmons from Area 2? Assume equal variance and use = 0.05. 6. Independent random samples are selected from two populations. The summary statistics are given below. Assume unequal variances for the questions below. m=5 n=7 x = 12.7 y = 9.9 s1 = 3.2 s2 = 2.1 a) Construct a 95% confidence interval for the difference of the means. b) Test if the means of the two populations are different based on the result from part (a). 7. Within a school district, students were randomly assigned to one of two Math teachers Mrs. Smith and Mrs. Jones. After the assignment, Mrs. Smith had 30 students, and Mrs. Jones had 25 students. At the end of the year, each class took the same standardized test. Mrs. Smith's students had an average test score of 78, with a standard deviation of 10; and Mrs. Jones' students had an average test score of 85, with a standard deviation of 15. Test the hypothesis that Mrs. Smith and Mrs. Jones are equally effective teachers. Use a 0.10 level of significance. (Assume that student performance is approximately normal.)