Answer :
The test statistic for testing the claim of a population mean body temperature of 98.5 °F is approximately -0.169.
The value of the test statistic for testing the claim that the mean body temperature of the population is equal to 98.5 °F can be determined using the formula:
Test statistic
=
Sample mean
−
Population mean
Standard deviation
/
Sample size
Test statistic=
Standard deviation/
Sample size
Sample mean−Population mean
In this case, the sample mean is 98.3 °F, the population mean is 98.5 °F (as claimed), the standard deviation is 0.5 °F, and the sample size is 76. Plugging these values into the formula, we can calculate the test statistic.
Test statistic = (98.3 - 98.5) / (0.5 / sqrt(76)) ≈ -0.169
The test statistic is approximately -0.169 (rounded to two decimal places).
The test statistic measures the difference between the sample mean and the hypothesized population mean, in terms of the standard deviation and sample size. A negative test statistic indicates that the sample mean is slightly lower than the claimed population mean. By comparing this test statistic with critical values from the t-distribution at a 0.05 significance level, we can determine whether the difference is statistically significant or simply due to chance.
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