Question

Game Wizard A friend of yours is constantly bragging that he performs exceptionally well at a popular video game since he scores an average of 1500 points. You think he is not all that hot. Having taken a statistics class, you know that you can actually test to see whether or not your friend scores higher than other players of the game. You collect a random sample of scores from other players at the local arcade and get the following data:

            1475    1420    1250    1650    1450    1380    1390    1650    1290    1460  

Is your friend right? That is, is there evidence that other players average less than 1500 points per game?  Conduct a hypothesis test, state the type of test, state the conditions, state your mechanics ( p-value, and test statistic) , and make sure to state your conclusion in context of the problem.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1500
Alternative Hypothesis, Ha: μ < 1500

Type of test is single mean t test

conditions:

• In theory, the data should be drawn from a normal distribution or it is a large sample (need
to check that n ≥ 30 ). In practice, using the t-distribution is sufficiently robust provided
that there is little skewness and no outliers in the data. Look at a graph of the data.
• The data must be reasonably random.
• The sample must be less than 10% of the population.

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1441.5 - 1500)/(131.2345/sqrt(10))
t = -1.410

P-value Approach
P-value = 0.0961
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that other players average less than 1500 points per game

### Here, significance level is not given so, con=sidered 0.05