Statistics and Probability Answers

5. One study found that 130 out of 250 patient who used the LAMA drug said their weight could be reduced in a given time. Meanwhile, 128 out of 200 people who use NEW medicine admit that their weight has decreased in a specified time. State the hypothesis that you feel is appropriate to test whether there is a difference in the ability of OLD medicine and NEW medicine in weight loss? Test the hypothesis you have built in (i) at the significance level of 5%.

4. A food production company HaHa claims that the average fat content of their food products is less than that of its main competitors. A nutritionist wants to know the truth of HaHa's allegations. He bought 11 packs of HaHa food and measured the fat content in the food. It was found that the average fat content was 31.3 gm with a standard deviation of 2.1gm. While the average fat content of the 11 main competitor food packs is 33.2gm with a standard siding of 1.8gm. Assuming a normal population with the same standard deviation, test the HaHa company claim at a significance level of 5%.

3. The Ministry of International Trade and Industry would also like to see the impact of the earthquake and tsunami disaster that hit Japan on the average price of imported Toyota Estima cars. A ministry expert said that if it was found that more than 30% of used car dealers had lowered prices, then a strong conclusion could be drawn that there would be a significant impact on the decline in Toyota Estima car prices due to the disaster in Japan. Out of 200 samples of used car dealers it was found that only 50 had lowered the price and the rest did not. Test whether the price of imported Toyota Estima cars has decreased using 95% confidence level

2. Prior to the earthquake and tsunami tragedy in Japan, it was found that the price of imported used Toyota Estima were normally distributed with mean price of RM170,000. After the disaster that hit Japan many claimed that the mean price of imported used Toyota Estima had dropped sharply. Driven by curiosity and want to apply statistical knowledge, a group of students of the Faculty of Economics and Management (FEP) UKM conducted a survey at 25 used imported car shops and found that the average price of a Toyota Estima car is RM165,000 per unit with a standard deviation of RM15,000 . Has the claim of earthquake and tsunami disaster in Japan reduced the price of imported Toyota Estima cars? Test this claim with a significance level of 5%.

1. A trade union in a factory has proposed an extension of 10 minutes of rest to workers in the hope of increasing the daily productivity of the factory. Prior to the addition of rest time, the average productivity of each employee was 240 unit per day with a standard deviation of 25 unit per day. After an additional 10-minute break was implemented, the union recorded a productivity record for each employee for 30 days at random and found that the average productivity per employee was 251 unit per day. Is there evidence at the 5% significance level that the daily productivity of factory workers has increased?

Weekly sales of copy paper at Cubicle Suppliers are provided in the table below. Compute a three-period moving average, a three-period weighted moving average (most recent period 05, last two period = 0.3, last three period = 0.2) and an exponential smoothing forecast (initial forecast = 26, α = 0.2). Compute the MAD, MSE, MAPE for each forecasting method. Which model is more accurate for week 8 forecast? (please use 3 decimal points)

Week Sales (cases) Forecast
1 27 26
2 28
3 28
4 29
5 29
6 27
7 28
8

For a given week, a random sample of 30 hourly employees selected from a very large number of employees in a manufacturing firm has a sample mean wage of x̅ = $180.00, with a sample standard deviation of

An Urban council has installed 2000 lamps with mercury bulbs in the streets of town area. The lifetimes of these bulbs are normally distributed with a mean of 1200 burning hours and having a standard deviation of 200 hours.
(i) How many of these bulbs can be expected to fail.
(a) In the first 800 burning hours?
b) Between 900 and 1750 burning hours?
(c) 10 % of the bulbs would fail?
(d)150 bulbs are still in good condition?