4.11 Hypothesis Testing

Melanie is playing an online game which has two digital four-sided dice numbered 1 to 4. The pair of digital dice are rolled together three times and points are scored. High points are scored for rolling doubles this is when both dice land on the same number. 

The following table shows the distribution of the number of doubles scored in each set of three throws when the Melanie plays the game 400 times. 

Melanie suspects that the data can be modelled using a binomial distribution with the probability of rolling a double being 0.25. A  goodness of fit test is to be used with a 5% significance level to test Melanie’s suspicion. 

Melanie still suspects that the data can be modelled using a binomial distribution. A  goodness of fit test is to be used with a 5% significance level to test Melanie’s suspicion.

Gordon takes the bus to work at the same time each day and he records the time, in minutes, of each journey. He collates his data in the table below.

Time (t minutes)	Frequency
	6
	11
	17
	21
	14
	1

Gordon wants to use a  goodness of fit test with a 10% significance level to see whether the journey times can be modelled by a normal distribution.

The mean time of the sample is 25.3 minutes and the standard deviation for the sample is 7.38 minutes.