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# Quantitative Technique and Decision Making

### Question 1

a) A study in Batu Pahat General Hospital's on patient account division has compiled data on the age of accounts receivables. The data collected indicates that the age of the accounts follows a normal distribution with mean 28 days and standard deviation 8 days. Ahmad would like to know the probability of the accounts between 20 and 40 days old and the probability of the accounts which less than 30 days old. Shows the calculation of both problems.

(7 marks)

b) The length of time for long-distance telephone calls from Malaysia to Thailand has mean of 16 minutes and standard deviation of 4 minutes. Suppose a sample of 35 telephone calls is used to reflect on the population of all long-distance calls. Calculate the chance that the average of the 35 telephone calls is between 17 and 18 minutes.

(8 marks)

### Question 2

a) Bella’s aims to construct a confidence interval for the mean of a normal population with known standard deviation. List three factors that could help her in reducing the size of margin error. Then, she collects a random sample of size from a population and from the data collected she compute a 95% confidence interval for the mean of the population. Based on the same dataset, state one factor that could produce a new confidence interval with larger width (Hint: Larger margin of error) .

(5 marks)

b) A random sample of thirty firms dealing in wireless products were selected to determine the proportion of such firms that have implemented new software to improve productivity. It turned out that eight of the thirty have implemented such software. Compute a 95% confidence interval on p, the true proportion of such firms that have implemented new software. In other situation, suppose there is concern about whether or not the point estimate of p = 8/30 is accurate enough because the confidence interval around p is not sufficiently narrow. By using p as your estimate of p, calculate how many companies would need to be sampled to have a 95% confidence interval with a width of only 0.05.

(10  marks)

### Question 3

a) Aminah wish to perform the hypothesis testing versus  with . The sample size 25 was obtained independently from a population with standard deviation 10. State the distribution of the sample mean given that null hypothesis is true and find the critical value, then calculate the values of sample mean if she reject the null hypothesis. Finally, compute the p-value, if the sample mean is -2.

(10 marks)

b) In one of the hypothesis study, Robin considers to increase the alpha level. Briefly explain the effect on the Type I and Type II errors together with the probability weather he should reject the null hypothesis.

(5 marks)

### Question 4

Dyson Company in Senai Johor plans to produce a new hair product known as Dyson Supersonic. The suppliers for the company are Company A and Company B found that 1% and 2% defective of 200 and 300 items respectively. Arrange appropriate hypothesis testing to investigate weather Company B are better by using 0.05 level of significance.

(15 marks)

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