High School

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.

Answer :

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:

  • Null hypothesis (H0): μ = 98.6°F
  • Alternative hypothesis (H1): μ ≠ 98.6°F

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.

Other Questions