**Title: Hypothesis Testing for Exam Score Averages****Context:**The average final exam score for the statistics course is 81%. A professor is investigating whether students who are provided with colored pens on the first day of class perform better. The final exam scores for a sample of 16 students, who received colored pens, are listed below. Assume a normal distribution of the population.**Sample Scores:**81, 81, 96, 78, 92, 94, 87, 92, 75, 87, 69, 98, 68, 95, 98, 92**Research Question:**What can be concluded at the α = 0.05 level of significance?**Steps to Follow:**a. **Test Selection:** - Determine the appropriate statistical test to use.b. **Hypotheses:** - Null Hypothesis ($H_0$): Define using the drop-down options. - Alternative Hypothesis ($H_1$): Define using the drop-down options.c. **Test Statistic:** - Calculate the test statistic (show answer to 3 decimal places).d. **P-Value:** - Determine the p-value (show answer to 4 decimal places).e. **Comparison:** - Compare the p-value to α.f. **Decision:** - Based on the comparison, decide whether to reject the null hypothesis.g. **Conclusion:** - Choose the correct conclusion from the options provided: 1. The data suggests the population mean is significantly higher than 81 at α = 0.05. 2. The data suggests the population mean is not significantly higher than 81 at α = 0.05. 3. The data suggests the population mean final exam score for students with colored pens is not significantly higher than 81 at α = 0.05. **Note:** Each step must be followed carefully to draw a reliable conclusion about the effectiveness of providing colored pens to improve exam scores.

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The Student's t-test is used for testing significance of difference between sample mean x¯ and…

Math

Statistics

The average final exam score for the statistics course is 81%. A professor wants to see if the a exam score for students who are given colored pens on the first day of class is higher. The fina for the 16 randomly selected students who were given the colored pens are shown below. AssL distribution of the population is normal. 81, 81, 96, 78, 92, 94, 87, 92, 75, 87, 69, 98, 68, 95, 98, 92 What can be concluded at the the a = 0.05 level of significance level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Но: 2 Select an answer H1: ? Select an answer c. The test statistic ? (please show your answer to 3 decimal places.)

The average final exam score for the statistics course is 81%. A professor wants to see if the a exam score for students who are given colored pens on the first day of class is higher. The fina for the 16 randomly selected students who were given the colored pens are shown below. AssL distribution of the population is normal. 81, 81, 96, 78, 92, 94, 87, 92, 75, 87, 69, 98, 68, 95, 98, 92 What can be concluded at the the a = 0.05 level of significance level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Но: 2 Select an answer H1: ? Select an answer c. The test statistic ? (please show your answer to 3 decimal places.)

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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Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

**Title: Hypothesis Testing for Exam Score Averages**

**Context:**
The average final exam score for the statistics course is 81%. A professor is investigating whether students who are provided with colored pens on the first day of class perform better. The final exam scores for a sample of 16 students, who received colored pens, are listed below. Assume a normal distribution of the population.

**Sample Scores:**
81, 81, 96, 78, 92, 94, 87, 92, 75, 87, 69, 98, 68, 95, 98, 92

**Research Question:**
What can be concluded at the α = 0.05 level of significance?

**Steps to Follow:**

a. **Test Selection:**
- Determine the appropriate statistical test to use.

b. **Hypotheses:**
- Null Hypothesis ($H_0$): Define using the drop-down options.
- Alternative Hypothesis ($H_1$): Define using the drop-down options.

c. **Test Statistic:**
- Calculate the test statistic (show answer to 3 decimal places).

d. **P-Value:**
- Determine the p-value (show answer to 4 decimal places).

e. **Comparison:**
- Compare the p-value to α.

f. **Decision:**
- Based on the comparison, decide whether to reject the null hypothesis.

g. **Conclusion:**
- Choose the correct conclusion from the options provided:
1. The data suggests the population mean is significantly higher than 81 at α = 0.05.
2. The data suggests the population mean is not significantly higher than 81 at α = 0.05.
3. The data suggests the population mean final exam score for students with colored pens is not significantly higher than 81 at α = 0.05.

**Note:** Each step must be followed carefully to draw a reliable conclusion about the effectiveness of providing colored pens to improve exam scores.

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