A random sample of 10 independent healthy people showed the following body temperatures (in degrees Fahrenheit):

1) 98.2
2) 98.2
3) 99.0
4) 96.9
5) 98.5
6) 98.9
7) 97.7
8) 99.1
9) 98.7
10) 97.9

Test the hypothesis that the population mean is not 98.6°F, using a significance level of 0.05.

Question

High School

Thank you for visiting A random sample of 10 independent healthy people showed the following body temperatures in degrees Fahrenheit 1 98 2 2 98 2 3 99 0. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Answer :

kashishAg78 kashishAg78 · Answer 1 · 2024-02-02T09:54:20-05:00

At the 0.05 significance level, we do not have sufficient evidence to conclude that the true mean body temperature is different from 98.6°F.

State the hypotheses:

Calculate the sample mean (x), sample standard deviation (s), and sample size (n):

Sample data: 98.2, 98.2, 99.0, 96.9, 98.5, 98.9, 97.7, 99.1, 98.7, 97.9
n = 10, x = (98.2 + 98.2 + 99.0 + 96.9 + 98.5 + 98.9 + 97.7 + 99.1 + 98.7 + 97.9) / 10 = 98.31°F
s = 0.684°F

Compute the test statistic:

Since the population standard deviation is unknown, we use the t-distribution. The test statistic is calculated as:

t = (x - μ) / (s/√n) = (98.31 - 98.6) / (0.684/√10) = -1.354

Determine the critical value (tcritical) for a two-tailed test at α = 0.05 and 9 degrees of freedom (n - 1):

From the t-distribution table, tcritical ≈ ±2.262

Compare the test statistic to the critical value:

Since -1.354 lies between -2.262 and 2.262, we fail to reject the null hypothesis.