Question

A research group wants to know if the online platform to play Settlers of Catan is being accessed more after the stay at home order than before it. The mean for number of games started per minute before the stay at home order was 1000. The researchers hypothesize that after the stay at home order, the online platform was accessed more so than before the stay at home order. They set alpha = .05 The mean for number of games started per minute after the stay at home order, was 1378 with a standard deviation of 489. The sample size was 108,000.

c. Please calculate the correct test statistic (show all your work) (2 points)

d. Please compare the test statistic to the correct value (alpha or critical value – mention which one you choose) and either reject or fail to reject the null hypothesis. Write out what this means in English (e.g. The test statistic … the … value, so we …. the null hypothesis. This means that after the stay at home order, the online platform to play Catan…) (2 points)

Answer 1

c) As we are testing here whether the mean is more than 1000, therefore the hypothesized mean value here is 1000. The test statistic now is computed here as:

Therefore 254.04 is the required test statistic value here.

d) For 0.05 level of significance, as this is an upper tailed test, we have from the standard normal tables:
P( Z > 1.645) = 0.05

Therefore 1.645 is the required critical value here.

As the test statistic value here is much more than critical value of 1.645, therefore the test is significant and we can reject the null hypothesis here. Therefore we have sufficient evidence here that after the stay at home order, the online platform was accessed more so than before the stay at home order.