Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion Test the claim that for the population of history exams, the mean score is 80. Sample data are summarized as n = 16, = 84.5, and s= 11.2. Use a significance level of a = 0.01. Select the correct test statistic and critical value.

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Assume that a simple random sample has been selected from a normally distributed population. 

**Problem Statement: Hypothesis Testing for a Population Mean**

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion.

**Task**: Test the claim that for the population of history exams, the mean score is 80. Sample data are summarized as follows:
- Sample size (\(n\)) = 16
- Sample mean (\(\bar{x}\)) = 84.5
- Sample standard deviation (\(s\)) = 11.2
- Significance level (\(\alpha\)) = 0.01

Select the correct test statistic and critical value.

**Options**:
1. Test statistic: \(z = 1.607\). Critical values: \(z = -2.947\).
2. Test statistic: \(t = -1.607\). Critical values: \(t = -2.947\).
3. Test statistic: \(t = 1.607\). Critical values: \(t = \pm2.947\).
4. Test statistic: \(t = 1.607\). Critical values: \(t = 2.947\).

**Note**: This question involves choosing the correct statistical test and understanding critical values to evaluate a claim about the population mean in a hypothesis test.
Transcribed Image Text:**Problem Statement: Hypothesis Testing for a Population Mean** Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. **Task**: Test the claim that for the population of history exams, the mean score is 80. Sample data are summarized as follows: - Sample size (\(n\)) = 16 - Sample mean (\(\bar{x}\)) = 84.5 - Sample standard deviation (\(s\)) = 11.2 - Significance level (\(\alpha\)) = 0.01 Select the correct test statistic and critical value. **Options**: 1. Test statistic: \(z = 1.607\). Critical values: \(z = -2.947\). 2. Test statistic: \(t = -1.607\). Critical values: \(t = -2.947\). 3. Test statistic: \(t = 1.607\). Critical values: \(t = \pm2.947\). 4. Test statistic: \(t = 1.607\). Critical values: \(t = 2.947\). **Note**: This question involves choosing the correct statistical test and understanding critical values to evaluate a claim about the population mean in a hypothesis test.
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