How to solve the following questions?
9:19 745 Major Assignment 10 Marks Question#1: The Standard deviation for a two liter bottle is 0.05, A random sample of 100 bottles shows that the average amount poured into a bottle is 1.59 liters. What is the 90% confidence Interval estimate of the true mean amount in 2-liter bottles? Question #2: A sample of 15 test tubes tested for number of times they can be beated on Bunsen burner before they cracked gave average of 1230 and standard deviation of 270. Construct a 90%% confidence interval for variance. Question #3: If 100 randomly selected nanners from a race can complete a mile run with an average time of 9 minutes with a standard deviation of 30 seconds. Find a 99% confidence interval for the Average time on all the runners in the race. Question#4: The Average IQ for the adult is 100 with a standard deviation of 13. A researcher believes this value has changed. The researcher decides to test the 19 of 75 random adults. The average DO of the sample is 105. Is there enough evidence to Suggest the average IQ has changed? Use 0.05 level of significance. Question#5: An e-commerer research company claims that 60% or more graduate students have bought merchandise on line. A consumer group is suspicious of the claim and thinks that the proportion is lower than 60% A random sample of 80 graduate students show that only 22 students have ever done so. Is there enough evidence to show that the true Proportion is lower than 6047 Conduct the test at 10% level of significance. Question#6: 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 35 students. At the end of the year, each class book the same Mandardized test. Mrs. Smith's students had an average test score of 78, with a standard deviation of 10; and Mrs. Jones' Mudents 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 05 level of significance. Question #7: The Acme Company has developed a new battery. The engineer in charge claims that the new battery will operate continuously for at least 7 minutes longer than the old battery. To test the claim, the company selects a simple random sample of 100 new batteries and 100 old batteries. The old batteries run on the average continuously for 190 minutes with a standard deviation of 20 minutes, the new batteries on the average 200 minutes with a standard deviation of 40 minutes. Test the engineer's claim that the new batteries run at least 7 minutes longer than the old. Use a 0.05 level of significance. Question#8: With individual lines at its various windows, a post office finds that the variance for normally distributed waiting times for customers on Friday afternoon is 30 minutes. The post oflice experiments with a single main waiting line and finds that
