Reference no: EM132824488

Problem 1 - Feasibility of a canteen facility

An appliance factory in the United States would like to estimate how much its factory workers spend per week to purchase lunch meals. This is to help in determining whether it would be worthwhile to open and operate its own canteen facility. The Chief Operating Officer was advised by a senior data analyst that spending per week on lunch meals follows a normal distribution. A random sample of 36 workers who purchase lunch meals were surveyed. It revealed that on average they paid $95 per week in buying lunch meals with a standard deviation equal to $11.5. Estimate with 95% confidence the actual mean spending on lunch meals per week for all of the factory workers.

a) Suppose you were a junior data analyst working for the factory. Which formula would you select to use in solving the problem? Provide a brief reason on your selection.

b) Obtain the lower confidence limit and the upper confidence limit of the 95% confidence interval estimate of the mean spending on lunch meals per week for all of the factory workers. Display working.

c) Present an interpretation of the lower confidence limit and the upper confidence limit obtained in part b) in the context of the problem.

d) Experience shows that operating canteen facilities in factories would be worthwhile if workers spend more than $100 per week on average to purchase lunch meals. Taking into consideration this statement and the results of the estimation you conducted in part b), present brief statements of two or three sentences to the Chief Operating Officer of the factory on whether or not it should open its own canteen facility. Yes or no? Why?

e) What would happen to the width of the interval when there is an increase in the value of the standard deviation? Assume all of the other variables to do the calculation of confidence interval held constant.

Problem 2 - Monitoring toddlers' weight

Monitoring the wellbeing of newborns is important in United Kingdom. Paediatricians follow closely the physical development of newborns until they reach a certain age. Parents are required to bring their babies and toddlers for a regular check-up which include a compulsory measurement of their height and weight. Weights of 24-month-old toddlers are normally distributed with a mean of 26.8 pounds and a standard deviation of 4.5 pounds.

a) Find the probability that a randomly selected 24-month-old toddler would have a weight at least 25 pounds. Display working.

b) The 5% heaviest 24-month-old toddlers would weigh at least how much (in pounds)? Display working.

c) A paediatrician randomly selected nine 24-month-old toddlers. What is the probability that the mean weight of those nine toddlers would be less than 24.8 pounds? Display working.

d) Further, the paediatrician randomly selected eight other 24-month-old toddlers. What is the probability that the mean weight of these eight selected toddlers would be between 25 pounds and 29 pounds? Display working.

Problem 4 - Should more economics lecturers be recruited?

The Program Director of a business degree in a public university is responsible for the learning experience of 1,230 new students recently enrolled. He is committed to recruit more lecturers in the economics discipline if more than 8% of his new students are likely to elect economics as a study major. To investigate this, the Program Director commissioned for a survey to be conducted amongst 300 randomly selected new students. They were asked which major they are likely to choose. 33 students identified economics as their most preferred major.

a) Suppose you were a post-graduate student working as the research assistant of the Program Director. Assist in performing a hypothesis test at the 10% level of significance to address the problem specified above. Display the six steps process (involving drawing the rejection region/s and determining the critical value/s for the decision rule) in performing the test.

b) Specify the decision rule to use in the p-value method hypothesis testing. Calculate the p-value of the test above. Display working.

c) Following the completion of the test in part a), would you suggest to the Program Director to recruit more economics lecturers? Yes or no? Why?

d) What is the required condition for ensuring that the sampling distribution of the sample proportion is approximately normally distributed? Check if the condition is satisfied in the hypothesis testing that you just completed.