Answer :
The value of the test statistic for this testing is approximately 2.84 (rounded to two decimal places).
Understanding Hypothesis Testing
To test the claim that the mean body temperature of the population is equal to 98.5 °F, we can perform a one-sample z-test. The test statistic can be calculated using the formula:
z = [tex]\frac{\bar{x} - \mu}{\sigma / \sqrt{n}}[/tex]
where:
[tex]\bar{x}[/tex] is the sample mean,
μ is the population mean under the null hypothesis,
σ is the population standard deviation,
n is the sample size.
Given:
[tex]\bar{x}[/tex] = 98.7 oF (sample mean),
μ = 98.5 oF (population mean under the null hypothesis),
σ = 0.5 oF (known population standard deviation),
n = 69 (sample size),
α = 0.05 (significance level).
Substituting the values into the formula, we get:
z = (98.7 - 98.5) / (0.5 / √69)
= 0.2 / (0.5 / √69)
= 0.2 * (√69 / 0.5)
≈ 2.84
Learn more about hypothesis testing here:
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