Test the claim that the mean body temperature is less than 98.6 using a=0.05. assume a sample of 16 yielded a mean of 98.2 with a standard deviation of 0.6
Use the same method as given in later post, but since you only have SD for sample, use that in the divisor.
Z = difference between means/√SE^2
I hope this helps. Thanks for asking.
To test the claim that the mean body temperature is less than 98.6 degrees, we can use a one-sample t-test with the given information.
Here are the steps to perform the hypothesis test:
Step 1: State the null and alternative hypotheses.
The null hypothesis (H0) is that the mean body temperature is equal to 98.6 degrees.
The alternative hypothesis (Ha) is that the mean body temperature is less than 98.6 degrees.
H0: μ = 98.6
Ha: μ < 98.6
Step 2: Determine the significance level (α).
The significance level (α) is given as 0.05 in this case.
Step 3: Collect the sample data and calculate the t-value.
In this case, a sample of 16 body temperatures yielded a mean of 98.2 degrees with a standard deviation of 0.6 degrees.
Step 4: Calculate the test statistic.
The test statistic for a one-sample t-test is given by:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Using the given data:
t = (98.2 - 98.6) / (0.6 / sqrt(16))
t = -0.4 / (0.6 / 4)
t = -0.4 / 0.15
t = -2.67 (rounded to two decimal places)
Step 5: Determine the critical value.
Since the alternative hypothesis is one-tailed (less than), we need to find the critical value for a one-tailed t-test with a degree of freedom (df) equal to the sample size minus 1 (n - 1).
At a significance level of 0.05 and df = 16 -1 = 15, the critical value is -1.753.
Step 6: Make a decision and interpret the result.
Compare the calculated t-value (-2.67) with the critical value (-1.753). If the calculated t-value is less than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
Since -2.67 < -1.753, we reject the null hypothesis.
Step 7: State the conclusion.
Based on the hypothesis test, with a sample of 16 body temperatures, a mean of 98.2 degrees, and a standard deviation of 0.6 degrees, there is sufficient evidence to conclude that the mean body temperature is less than 98.6 degrees at a significance level of 0.05.