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MATH1127: Introduction to Statistics (60022) Lesson 9.4 Rare Events, the Sample, Decision and Conclusion
Unit 3 Chapter 9: Lesson 9.4 Assignment
It is commonly believed that the mean body temperature of a healthy adult is $98.6^{\circ} \mathrm{F}$. You are not entirely convinced. You believe that it is not $98.6^{\circ} \mathrm{F}$. You collected data using 45 healthy people and found that they had a mean body temperature of $98.21^{\circ} \mathrm{F}$ with a standard deviation of $1.13^{\circ} \mathrm{F}$.
Use a 0.05 significance level to test the claim that the mean body temperature of a healthy adult is s $98.6^{\circ} \mathrm{F}$.
a) Identify the null and alternative hypotheses?
\[
H_{0}: ? \quad v
\]
\[
H_{A}: ? \vee
\]
b) What type of hypothisis test should you conduct (left-, right-, or two-tailed)?
left-tailed
right-tailed
two-tailed
c) Identify the appropriate significance level.
d) Calculate your test statistic. Write the result below, and be sure to round your final answer to 3 decimal places.
e) Calculate your p-value. Write the result below, and be sure to round your final answer to 3 decimal
IMG_2842.jpg
IMG_2841.jpg
IMG_2840.jpg
Answer
Final Answer: \[H_{0}: \mu = 98.6^{\circ} \mathrm{F}\] \[H_{A}: \mu \neq 98.6^{\circ} \mathrm{F}\]
Step 1 ：The null hypothesis (H0) is a statement of no effect or no difference. In this case, the null hypothesis would be that the mean body temperature of a healthy adult is 98.6°F.
Step 2 ：The alternative hypothesis (HA) is what you might believe to be true or hope to prove true. In this case, the alternative hypothesis would be that the mean body temperature of a healthy adult is not 98.6°F.
Step 3 ：Final Answer: \[H_{0}: \mu = 98.6^{\circ} \mathrm{F}\] \[H_{A}: \mu \neq 98.6^{\circ} \mathrm{F}\]
