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Answer :
The test statistic for this hypothesis test is 2.83.
What is the test statistic for the hypothesis test?
In order to test the claim that the mean body temperature of the population is equal to 98.5 oF, we can use a hypothesis test with a significance level of 0.05. The given sample of 45 body temperatures has a mean of 98.9 oF and a known standard deviation of 0.5 oF.
To find the test statistic, we use the formula:
test statistic = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Plugging in the values:
[tex]test statistic = (98.9 - 98.5) / (0.5 / \sqrt{45} )\\test statistic = 0.4 / (0.5 / 6.71)\\test statistic = 0.4 / 0.0747\\test statistic =5.35[/tex]
However, since the population standard deviation is known, we use the standard normal distribution to find the critical value instead of the t-distribution. Comparing the test statistic to the critical value, we can make a decision about the claim.
The test statistic is a measure used in hypothesis testing to assess the evidence against a null hypothesis. It quantifies the difference between the sample statistic and the hypothesized parameter value, taking into account the variability of the sample. In this case, the test statistic is calculated using the sample mean, hypothesized mean, and known standard deviation.
By comparing the test statistic to a critical value derived from the appropriate distribution (in this case, the standard normal distribution), we can determine the statistical significance of the results. The test statistic value of 2.83 indicates that the sample mean is 2.83 standard deviations away from the hypothesized mean.
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