You are given a sample of 106 body temperatures having a mean of 98.2 F and a standard deviation of 0.62 F. You are asked to test the hypothesis that the population mean body temperature is 98.6 F using a 0.05 significance level. What value should you use for the test statistic?
The answer is -6.64 but I'm confused as to how it was found. Please help. I'm studying for a final.
This is what I would do.
Z = (score-mean)/SEm
SEm = SD/√n
P ≤ .05
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. How does it compare?
To test the hypothesis that the population mean body temperature is 98.6 F, you can use a one-sample t-test. The test statistic for this hypothesis test is the t-score.
The formula for calculating the t-score is:
t = (x̄ - μ) / (s / √n)
Where:
- x̄ is the sample mean (98.2 F in this case)
- μ is the hypothesized population mean (98.6 F in this case)
- s is the sample standard deviation (0.62 F in this case)
- n is the sample size (106 in this case)
Using the given values, we can substitute them into the formula to calculate the t-score:
t = (98.2 - 98.6) / (0.62 / √106)
Calculating the numerator first:
98.2 - 98.6 = -0.4
Then, calculating the denominator:
0.62 / √106 ≈ 0.06031
Dividing the numerator by the denominator, we get:
t ≈ -0.4 / 0.06031 ≈ -6.64
Therefore, the test statistic for this hypothesis test is approximately -6.64.
Remember that the test statistic helps determine the likelihood of observing the given sample mean under the assumption of the null hypothesis (that the population mean is 98.6 F), assuming that the data follows a t-distribution.