After googling this question, I couldn't find any advice that was actually free, so I wanted to ask here. It's a review question and I'm trying to prepare for my finals next week. I'm just wondering if my steps for this problem were correct.
The question is: A medical scientist believes that the average basal temperature of (outwardly) healthy individuals has increased over time and is now greater than 98.6 degrees Fahrenheit. To prove this, she has randomly selected 100 healthy individuals. If their mean temperature is 98.74 with a sample standard deviation of 1.1 degrees, does this prove her claim at the 5 percent level? What about the 1 percent level?
I've only attempted the 5% portion since I'm not sure if I'm correct. Nonetheless, here I go:
The population mean is: 98.6
n = 100 people in the survey
average temperature of those people: 98.74
std dev: 1.1
The level of significance(?) is .05. Therefore, the value from the table (z-dist table) would be 1.96.
Based on the values, I used this formula:
z = |x-bar - pop. mean| / (stdDev / sqrt(n) )
After plugging in the values, I got:
p-value = P(hypothesis)( z > 1.27)
Now I do a check: 1.27 > 1.96, which is not true. Therefore, we can't reject the hypothesis that the average basal temperature has risen.
Is this the correct line of reasoning? If not, then could someone please tell me where I went wrong? Explanations are always nice.