## Question 873:

1## Answer:

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You want to perform a 1-sample t-test here using the 1-tailed probabilities. The clue to tell you that you should use a 1-sample t test is the inclusion of the criteria or benchmark for 3.50 hours and that there is only one sample of data. We want to use a 1-tailed version of this test because we're asked whether the sample of data provides evidence that the population average game time is less than 3.5 hours.The Null Hypothesis is that the average game time is more than 3.50 hours. We will reject the Ho if our p-value is less than .05. Using the critical value method we will reject the Ho if our test statistic is greater than 1.74. The 1.74 is found from looking up the critical value from the t-distribution on 16 degrees of freedom (n-1) for an alpha of .05 and for 1-tailed probabilities. You can also use the excel formula =TINV(.10, 16).

From the 17 game times we get a mean time of 2.96 hours with a standard deviation of .559. The test statistic is equal to difference between the sample mean and test mean (3.50-2.96) = .554 divided by the standard error (SE). The SE is equal to the standard deviation divided by the square root of the sample size (.559/SQRT(17) = .1357.

We can then see than a difference of .554 hours is more than 4 standard errors from the test mean (.554/.1357) = -4.01. The p-value is less than .01 so we reject the Null. We have enough evidence to conclude that the mean game time is less than 3.50 hours.

See the attached excel file for the calculations.