Sometimes when you are sick, your forehead feels really warm. You might have fever. How can you find out whether you do? By taking your temperature , of course. But what temperature should the thermometer show if your're healthy? Is this temperature the same for everyone?

Sometimes when you are sick, your forehead feels really warm. You might have fever. How can you find out whether you do? By taking your temperature , of course. But what temperature should the thermometer show if your're healthy? Is this temperature the same for everyone? 

Several years ago, researchers conducted a study to determine whether the "accepted" value for normal body temperature, 98.6^oF, is accurate. They used an oral thermometer to measure the temperatures of a random sample of healthy men and women aged 18 to 40. As is often the case, the researchers did not provide their original data. 

Allen Shoemaker, from Calvin College, produced a data set with the same properties as the original temperature readings. His data set consists of one oral temperature reading for each of the 130 randomly chosen, healthy 18- to 40-year-olds. A dotplot of Shoemaker's temperature data is shown below. A vertical line at 98.6^oF was added for reference. 

Exploratory data analysis revealed several interesting facts about this data set:

• The mean temperature was x ¯ = 98.25 o F
• The standard deviation of the temperature reading was s x = 0.73 o F
• 62.3% of the temperature readings were less than 98.6^oF. 

If "normal" body temperature really is 98.6^oF, we would expect that about half of all healthy 18- to 40-year-olds will have a body temperature less than 98.6^oF. Do the data from this study provide convincing evidence at the α = 0.05 significance level that this is not the case? 

1. 1. What type of significance test would you run given the data above? 
   2. What conditions must be satisfied for the test you have chosen in order to get valid results? Are the conditions satisfied? 
   3. Run your test for significance using the data link above. Attach the data output including the hypotheses that you have chosen.
   4. Using the p-value (or critical values & test statistic), draw a proper conclusion and write said conclusion in context. 
   5. Based on your conclusion, which type of error could have been made: a Type I error or a Type II error. Justify your answer. 
   6. If you were a researcher, what type of data would you be interested in collecting? What would your null and alternative hypotheses be?