The Study
The samples that I collected was by logging on to Wordament and actually playing a round in order to see the person who scored the most points to get the word count. My population of intrest was anyone playing the English boards of Wordament placing first. The samples where collected throughout the day as evenly as possible. This is due to the amount of players that plays Wordament may vary to time of day and day-to-day. Even though there is no association between the two. I was able to capture 110 rounds of Wordament.
Link to Raw Data
The 1-Sample mean T-test was used to test if 80 words is enough to win a round of Wordament. There are no other groups of means to test, therefore, the 1-sample mean test is the best test to use for this study.
x= The average words found by the winner.
The null hypothesis is the sample mean is equal to 80. Ho: x=80.
The alternative hypotheses is the sample mean is greater than 80. Ha: x>80.
The level of significance will be at 95%. α = 0.05 This is due to since there are no variables that causes errors will not be significant to anyone's health.
Conditions:
The samples were chosen randomly by logging onto Wordament and play a round.
The sample size is 110 rounds. Since 110 is greater than or equal to 30, the Central Limit Theroem applies.
I can saflely assume that the sample size is less than 10% of the population. Wordament was released in 2011, therefore, many rounds have been played since 2011. There are over 40,000,000,000,000,000,000,000 boards and configurations in Wordament.
t=
t=17.48 p=0.000 df=109
Conlusion: I reject that the null hypothesis at any resonable level of significance since the p-value of essentially 0 is less than alpha. Therefore, there is enough evidence to conclude that the number of words found by the winner is greater than 80 words.