Using the data below, complete the following:
Recall that:
Type I error is defined as rejecting the null hypothesis when in fact it should not be rejected (i.e., "false positive," "false alarm," defendant found guilty when in fact innocent).
Type II error is defined as not rejecting the null hypothesis when in fact it should be rejected (i.e., "false negative," defendant found not guilty when in fact guilty).
In the context of the below hypothesis test, discuss what the type I error and type II error would mean, using a decision table as your guide.
My restaurant has been very successful in the United States, and I would like to expand internationally to assess potential customers better and if my restaurant will be successful in another country. My home country is the United States, and I would like to expand to Germany.
Count of Importances of friends rating [Column Labels] Row Labels TNA Not at All Important Not Very Important Somewhat Important Very Important Grand Total Germany 117 892 1029 2046 NA 2 Not at All Important 118 274 Not Very Important m m m NRM 411 539 Somewhat Important 286 745 Very Important 3 4 3 96 186 United States 19 1235 2232 NA Not at All Important Not Very Important 324 378 746 Somewhat Important 954 Very Important 270 Grand Total 19 24 221 1750 2264 4278
I will compare percentages at the intersection of friends are somewhat important and very important. To do that for the United States, I will sum up 568+176=744, which gives a fraction of 744/1235 = 0.602 or 60.2%.
I will also compare the percentages at the intersection of friends are somewhat important and very important in the new country Germany. I sum up 423+96=519, which gives a fraction of 519/1029 = 0.504 or 50.4%.
For my current country:
Ho: p = 0.602
Ha: p < 0.602
Based on this hypothesis, I have a one-tailed lower test because we fail to reject the null hypothesis!
Since my focus for my business is a place where friends can be and have fun, this hypothesis states that friends are less important in Germany than in the United States. The percentage is not too far off, but I'm not sure if this would be a safe move.
