Question 1. The manager of a factory claims that his workers take at most 10 minutes to finish a task. A random sample of 15 workers gave a mean time of 12.5 minutes and a standard deviation of 3.4 minutes. Assume that the time taken to complete the task is normally distributed. Test whether the manager's claim is true at a 10% significance level.

Question 2. A road safety survey reports that 35% of private car passengers wear seatbelts. A recent survey done on a random sample of 80 private car passengers found that 32 of them wore seatbelts. Test whether there is sufficient evidence to conclude that there is a change in the proportion of private car passenger who wears a seatbelt at a 5% significance level

Question 3. A hair salon owner wishes to determine if the preferred brand of shampoo of her customers is independent of gender. The table below shows the sample record of her customers. Gender Prefer brand of shampoo Brand A Brand B Brand C Male 12 18 10 Female 35 12 13 Test whether the preferred brands of shampoo of the customers are independent of gender at a 10% significance level

Question 4. Past records of a real estate company show that 40% of the rented properties in city A are serviced apartments, 30% are condominiums, 20% are terrace houses, and 10% are other types of properties. The table below shows the results of a recent survey of 120 customers on their preferred type of rented property. Type of property Serviced Apartment Condominium Terrace House Others Number of customers 34 44 18 24 Test to determine whether there is a change in the distribution of the preferred type of rented property among the customers at a 5% significance level.