Answer :
Final answer:
Based on the hypothesis test with a 10% alpha level, we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the true average temperature of COVID patients is different from the sample average temperature of 101.2.
Explanation:
To test if the true average temperature of COVID patients is different from the sample average temperature, we will perform a hypothesis test using the known population standard deviation.
Null Hypothesis (H0): The true average temperature of COVID patients is equal to 101.2.
Alternative Hypothesis (Ha): The true average temperature of COVID patients is not equal to 101.2.
We will use a significance level (alpha) of 0.10, which means we are willing to accept a 10% chance of making a Type I error (rejecting the null hypothesis when it is true).
Next, we will calculate the test statistic using the formula:
test statistic = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
Substituting the given values:
sample mean = 101.2
population mean = 101.2
population standard deviation = 6
sample size = 56
Calculating the test statistic:
test statistic = (101.2 - 101.2) / (6 / sqrt(56))
Since the test statistic is 0, we can calculate the p-value using a t-distribution with (sample size - 1) degrees of freedom.
Finally, we compare the p-value to the significance level (alpha) to make a decision. If the p-value is less than alpha, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.
Learn more about hypothesis testing here:
https://brainly.com/question/33445215
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