Suppose researchers conducted a study to see if the mean body temperature for adults was different from 98.6 degrees Fahrenheit. For this study, they took a random sample of 25 healthy adults and found a mean body temperature of 98.2 degrees Fahrenheit for the sample with a standard deviation of 0.6 degrees. The temperatures of the sample participants were unimodal and symmetric. a. Write the null hypothesis and alternative hypothesis and define your parameter. b. Show that the necessary conditions (Randomization Condition, 10% Condition, Nearly Normal Condition) are satisfied to perform a hypothesis test. Briefly explain how each condition is satisfied. c. Perform the hypothesis test and find the P-value. (To show your work: Write down which calculator you are using and what values you are entering into the calculator.)

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Answer A B C and please follow the instructions

### Study on Mean Body Temperature of Adults

Researchers investigated whether the mean body temperature for adults deviates from the commonly accepted value of 98.6 degrees Fahrenheit. A random sample of 25 healthy adults yielded a mean body temperature of 98.2 degrees Fahrenheit with a standard deviation of 0.6 degrees. The sample data showed that the temperatures were unimodal and symmetric.

**a. Hypothesis Formulation:**
- **Null Hypothesis (\(H_0\))**: The mean body temperature for adults is 98.6 degrees Fahrenheit. (\(\mu = 98.6\))
- **Alternative Hypothesis (\(H_a\))**: The mean body temperature for adults is different from 98.6 degrees Fahrenheit. (\(\mu \neq 98.6\))

**b. Condition Verification:**
- **Randomization Condition**: The sample of 25 adults was randomly selected, which satisfies the randomization condition.
- **10% Condition**: The sample size (25 adults) is less than 10% of all adults, satisfying the 10% condition.
- **Nearly Normal Condition**: The sample distribution is unimodal and symmetric, which meets the nearly normal condition.

**c. Hypothesis Test and P-value Calculation:**
To perform the hypothesis test and calculate the P-value, follow these steps:
1. Use a statistical calculator or software.
2. Input the sample mean (\( \bar{x} = 98.2 \)), population mean (\( \mu = 98.6 \)), sample standard deviation (\( s = 0.6 \)), and sample size (\( n = 25 \)).
3. Use a T-test for the mean of a single sample.

Write down the values you input into the calculator and check the output to find the P-value.

**Note:**
Remember to use the appropriate settings and verify the results with the critical values from the T-distribution table corresponding to your degrees of freedom (\( n-1 \)) for double-checking your calculations.

By following these steps and verifying the conditions, you ensure a valid hypothesis testing procedure that will help you determine whether the mean body temperature for adults significantly differs from 98.6 degrees Fahrenheit.
Transcribed Image Text:### Study on Mean Body Temperature of Adults Researchers investigated whether the mean body temperature for adults deviates from the commonly accepted value of 98.6 degrees Fahrenheit. A random sample of 25 healthy adults yielded a mean body temperature of 98.2 degrees Fahrenheit with a standard deviation of 0.6 degrees. The sample data showed that the temperatures were unimodal and symmetric. **a. Hypothesis Formulation:** - **Null Hypothesis (\(H_0\))**: The mean body temperature for adults is 98.6 degrees Fahrenheit. (\(\mu = 98.6\)) - **Alternative Hypothesis (\(H_a\))**: The mean body temperature for adults is different from 98.6 degrees Fahrenheit. (\(\mu \neq 98.6\)) **b. Condition Verification:** - **Randomization Condition**: The sample of 25 adults was randomly selected, which satisfies the randomization condition. - **10% Condition**: The sample size (25 adults) is less than 10% of all adults, satisfying the 10% condition. - **Nearly Normal Condition**: The sample distribution is unimodal and symmetric, which meets the nearly normal condition. **c. Hypothesis Test and P-value Calculation:** To perform the hypothesis test and calculate the P-value, follow these steps: 1. Use a statistical calculator or software. 2. Input the sample mean (\( \bar{x} = 98.2 \)), population mean (\( \mu = 98.6 \)), sample standard deviation (\( s = 0.6 \)), and sample size (\( n = 25 \)). 3. Use a T-test for the mean of a single sample. Write down the values you input into the calculator and check the output to find the P-value. **Note:** Remember to use the appropriate settings and verify the results with the critical values from the T-distribution table corresponding to your degrees of freedom (\( n-1 \)) for double-checking your calculations. By following these steps and verifying the conditions, you ensure a valid hypothesis testing procedure that will help you determine whether the mean body temperature for adults significantly differs from 98.6 degrees Fahrenheit.
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