We are interested in testing for differences in the palatability of three spicy salsas: A, B, and C. For each product, a sample of 25 men was chosen. Each rated the product from –3 (terrible) to +3 (excellent).The following SAS output was produced.
The supervisor of security at a large department store would like to know whether the store apprehends relatively more shoplifters during the Christmas holiday season than in the weeks before or after the holiday. He gathered data on the number of shoplifters apprehended in the store during the months of November, December, and January over the past 6 years. The information follows:
An Introduction to Economics course is offered in 3 sections, each with a different instructor. The fi nal grades from the spring term are presented be low. Is there a signifi cant difference in the average grades given by the instructors? State and test appropriate hypotheses at α = 0.01.
The manufacturer of silicon chips requires so-called clean rooms, where the air is specially filtered to keep the number of dust particles at a minimum. The Outel Corporation wants to make sure that each of its fi ve clean rooms has the same number of dust particles. Five air samples have been taken in each room. The “dust score,” on a scale of 1 (low) to 10 (high), was measured. At the 0.05 level of significance, do the rooms have the same average dust score?
A lumber company is concerned about how rising interest rates are affecting the new housing starts in the area. To explore this question, the company has gathered data on new housing starts during the past three quarters for five surrounding counties. This information is presented in the following table. At the 0.05 level of significance, are there any differences in the number of new housing starts during the three quarters?
Genes-and-Jeans, Inc., offers clones of such popular jeans as Generic, DNA, RNA, and Oops. The store wants to see whether there are differences in the number of pairs sold of different brands. The manager has counted the number of pairs sold for each brand on several different days. At the 0.05 signifi cance level, are the sales of the four brands the same?
The Government Accounting Office (GAO) is interested in seeing whether similar-sized offices spend similar amounts on personnel and equipment. (Offices spending more are targeted for special auditing.) Monthly expenses for three offices have been examined: one office in the Agriculture Department, one in the State Department, and one in the Interior Department. The data follow. At the 0.01 significance level, are there differences in expenses for the different offices?
In Bigville, a fast-food chain feels it is gaining a bad reputation because it takes too long to serve the customers. Because the chain has four restaurants in this town, it is concerned with whether all four restaurants have the same average service time. One of the owners of the fast-food chain has decided to visit each of the stores and monitor the service time for five randomly selected customers. At his four noontime visits, he records the following service times in minutes:
LWP is a large multinational company, having more than 2000 employees under its payroll. The management of the LWP company has introduced an intensive and comprehensive training programme for its managerial level employees. There are four different types of training progammes, currently under consideration. Employees were divided into four groups and different groups were given different training programmes. Now the management of LWP wants to examine the effectiveness of these training programmes i.e. whether these programmes have been resulting into same managerial skill enhancement or their degree of effectiveness is different. Simultaneously, the management also wants to examine whether there is some change in the effectiveness – degree with the level of experience of employees. Management believes that these two factors are independent. There are 5 categories of experience-levels, as envisaged by the HR department of LWP. For this dual purpose, 20 employees were randomly chosen, according to a particular scheme. Five employees were chosen from each training programme and in each subgroup, 5 employees belong to 5 different experience categories. The employees thus selected were given a managerial-skill aptitude examination to examine their managerial aptitude and their scores are tabulated in form of following table:
The standard deviation of a distribution is hypothesized to be 50. If an observed sample of 30 yields a sample standard deviation of 57, should we reject the null hypothesis that the true standard deviation is 50? Use the 0.05 level of signifi cance