Question

A video game company is interested in knowing the population mean number of hours spent playing a new game from start to finish. If the game takes longer than 50 hours to play, on average, then it will need to be re-worked. The company collects a sample of 49 video game players with various levels of expertise and finds that it takes them 48 hours, on average, to complete the game, with a standard deviation of 1.5 hours.

1. Conduct an appropriate hypothesis test using the critical value method. [7 marks]
   
2. Explain what a Type II Error means in this context. [1 mark]
   

Answer 1

Solution:

a. The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Since the significance level is not given, let's assume it to be 0.05, therefore, the critical value is:

Conclusion: Since the test statistic is less than the critical value, we, fail to reject the null hypothesis and conclude that there is not sufficient evidence for them to rework on the game

b. The type II error is the error of failing to reject the null hypothesis when in fact it is not correct. So it means here the error of not reworking on the game when in fact it has to be reworked as it takes more than 50 hours to play