Activity 1

A. Write the null hypothesis and alternative hypothesis in notation of the following statements. 1. A bus company in Manila claims that the mean waiting time for a bus during rush hour is less than 12 minutes. A random sample of 30 waiting times has a mean of 15 minutes with a standard deviation of 4.8 minutes. H: 0 H : [t 2. The average power consumption of air conditioner is at most 2,700 watts as claimed by the owner. A survey made by an electric power company found out that the mean consumption is 3,000 with standard deviation of 225. H : 0 B. Identify whether the given hypothesis is one-tailed or two-tailed. Write ONE if it is one-tailed and TWO if it is two-tailed test. 1. A used car dealer says that the mean price car in the Philippines is at least P350000. 2. PAG-ASA reported that the mean annual rainfall in the Philippines is at most 4,064mm. 3. According to the survey, the average cost of visiting doctors is P500. 4. The mean age of students in a university in the previous years was 27 years old. An instructor thinks the mean age for students is older than 27. She randomly surveys 56 students and finds that the sample mean is 29 with a standard deviation of 2. 5. The mean work week for engineers in a new company is believed to be about 40 hours. A newly hired engineer hopes that it is shorter. She asks 10 engineering friends for the lengths of their mean work weeks. Based on the results, should she count on the mean work week to be shorter than 40 hours? C. Identify the appropriate test statistic to be used in each problem. Write z-test or t-test on a separate sheet of paper. ___________1. A sample of n=25 is selected from a normal population, x_= 56 and s= 12. 2. Based on the report of the school nurse, the average height of Grade 11 students has increased. Five years ago, the average height of Grade 11 students was 1YOcm with standard deviation of 380m. She took a random sample of 150 students and derived the average height of 1650m. 3. Knowing from a previous study that the average of athletes is 80, an athletic adviser asked how his soccer players are academically doing as compared to other student athletes. After an initiative to help improve the average of student athletes, the adviser randomly selected 15 soccer players and found 85 as the average with standard deviation of 1.25. 4. The CEO of a battery manufacturing company claimed that their batteries would last an average of 280 hours under normal use. A researcher randomly selected 20 batteries from the production line and tested them. The tested batteries had a mean life span of 250 hours with a standard deviation of 40 hours. Do we have enough evidence to suggest that the claim of an average of 280 hours is false? 5. It was known that the number of tickets purchased by students at the ticket window for the volleyball match of two popular universities followed a distribution that has mean of 500 and standard deviation of 8.9. Suppose that a few hours before the start of one of these matches, there are 100 eager students standing in line to purchase tickets. If there are 250 tickets remaining, what is the probability that all 100 students will be able to purchase the tickets they want