High School

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A sample of 93 body temperatures has a mean of 98.3. Assume that σ is known to be 0.5 oF. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.5 oF, as is commonly believed. What is the value of test statistic for this testing? (Round off the answer upto 2 decimal places)

Answer :

The test statistic in this problem is given as follows:

z = -3.86.

As the absolute value of the test statistic is greater than the critical value of z* = 1.96, there is enough evidence to reject the claim regarding the body temperature of the population.

How to calculate the test statistic?

The equation for the test statistic in this problem is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

  • [tex]\overline{x}[/tex] is the sample mean.
  • [tex]\mu[/tex] is the value tested at the null hypothesis.
  • [tex]\sigma[/tex] is the standard deviation of the population.
  • n is the sample size.

The parameters for this problem are given as follows:

[tex]\overline{x} = 98.3, \mu = 98.5, \sigma = 0.5, n = 93[/tex]

Hence the test statistic is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{98.3 - 98.5}{\frac{0.5}{\sqrt{93}}}[/tex]

z = -3.86.

More can be learned about the z-distribution at https://brainly.com/question/25890103

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