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 (\(\alpha\)) = 0.01Select 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.

given data n = 16x¯ = 84.5s = 11.2α = 0.01claim : μ = 80

Answered: Assume that a simple random sample has…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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