A certain Suppose a nutritionist believes that the true mean number of calories served at lunch at all schools in the country is below 1006 calories. a. Identify the parameter of interest. b. Specify the null and alternative hypotheses for testing this claim. c. Describe a Type I error in the words of the problem. d. Describe a Type Il error in the words of the problem. a. The parameter of interest is u.

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### Hypothesis Testing for School Lunch Program

In a national lunch program, a high school must ensure that the number of calories served at lunch complies with certain standards to receive reimbursement. It is mandated that the lunch should contain no more than 1000 calories. A nutritionist suspects that the true mean number of calories served at lunch at all schools in the country is below 1000 calories. The following steps outline how to statistically test this claim.

#### a. Identify the Parameter of Interest
The parameter of interest is the true mean number of calories (μ) served at lunch.

#### b. Specify the Null and Alternative Hypotheses
The hypotheses are formulated as follows:

- Null Hypothesis (H₀): μ = 1000
- Alternative Hypothesis (Hₐ): μ < 1000

#### c. Type I Error
A Type I error occurs when the null hypothesis is true, but we mistakenly reject it. In this context, a Type I error would mean concluding that the true mean number of calories served is below 1000 calories when, in fact, it is not.

#### d. Type II Error
A Type II error occurs when the null hypothesis is false, but we fail to reject it. Here, a Type II error would mean failing to recognize that the true mean number of calories served is below 1000 calories when it actually is.

### Hypotheses Completion
To complete the hypotheses notation:

- \( H_0: \mu = 1000 \)
- \( H_a: \mu < 1000 \)

By defining and testing these hypotheses, we aim to make an informed inference about the calorie content of school lunches and adhere to nutritional standards.
Transcribed Image Text:### Hypothesis Testing for School Lunch Program In a national lunch program, a high school must ensure that the number of calories served at lunch complies with certain standards to receive reimbursement. It is mandated that the lunch should contain no more than 1000 calories. A nutritionist suspects that the true mean number of calories served at lunch at all schools in the country is below 1000 calories. The following steps outline how to statistically test this claim. #### a. Identify the Parameter of Interest The parameter of interest is the true mean number of calories (μ) served at lunch. #### b. Specify the Null and Alternative Hypotheses The hypotheses are formulated as follows: - Null Hypothesis (H₀): μ = 1000 - Alternative Hypothesis (Hₐ): μ < 1000 #### c. Type I Error A Type I error occurs when the null hypothesis is true, but we mistakenly reject it. In this context, a Type I error would mean concluding that the true mean number of calories served is below 1000 calories when, in fact, it is not. #### d. Type II Error A Type II error occurs when the null hypothesis is false, but we fail to reject it. Here, a Type II error would mean failing to recognize that the true mean number of calories served is below 1000 calories when it actually is. ### Hypotheses Completion To complete the hypotheses notation: - \( H_0: \mu = 1000 \) - \( H_a: \mu < 1000 \) By defining and testing these hypotheses, we aim to make an informed inference about the calorie content of school lunches and adhere to nutritional standards.
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