Question

A video game manufacturer has recently released a new game. The manufacturer wants to know whether players rate their new game as more or less difficult than the average difficulty rating of all of their games, μ = 6 and σ = 2. A random sample of 36 players yielded a sample mean of 7 and a standard deviation(s) of 1.8.

             a. State the null and alternative hypothesis.

             b. Conduct a z-test on the data given.

             c. What do you conclude?

Answer 1

Given: = 6, = 7, = 2, n = 36, = 0.05 (default level)

The Hypothesis:

H0: = 6

Ha: 6

This is a 2 tailed test

The Test Statistic:

The test statistic is given by the equation:

The p Value:    The p value (2 Tail) for Z = 3 ,is; p value = 0.0026

The Critical Value:   The critical value (2 Tail) at = 0.05, Zcritical= +1.96 and -1.96

The Decision Rule:   If Zobservedis >Zcritical or if Zobserved is < -Zcritical, Then reject H0.

Also if P value is < , Then Reject H0.

The Decision:   Since Zobserved (3) is > Z critical (1.96), We Reject H0.

Also since P value (0.0026) is < (0.05) , We Reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that there is a difference in the difficulty than the average difficulty rating of all their games.