Forty-five percent of the entering CSUN freshmen in Fall 2019 were proficient in math. www.csun.edu/counts/new_first time_freshman.php a. You want to see if the percentage is different for this fall's entering freshmen. Ha: Your hypotheses are Ho: where stands for the percentage of freshmen who were proficient in Fall 2019/ this fall.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![**Transcription for Educational Website:**
**Question 2**
Forty-five percent of the entering CSUN freshmen in Fall 2019 were proficient in math.
[Source: www.csun.edu/counts/new_first_time_freshman.php]
**a. Hypothesis Testing:**
- **Objective:** Determine if the percentage differs for this fall's entering freshmen.
- **Hypotheses:**
- Null Hypothesis (Ho): __________
- Alternative Hypothesis (Ha): __________
*Note:* Here, \(p\) represents the percentage of freshmen proficient in math for Fall 2019/this fall.
**b. Sampling Distribution:**
- **Assumption:** Null hypothesis is true (45% proficiency this fall).
- **Below is the sampling distribution graph, based on repeated random samples of 150 freshmen this fall, which shows the proportion proficient in math.*
*Graph Explanation:*
- The bell curve represents a normal distribution of sample proportions.
- X-axis ranges from 0.33 to 0.57.
- Marked values are 0.33, 0.37, 0.41, 0.45, 0.49, 0.53, and 0.57.
- Center of the distribution is at 0.45.
*Tasks:*
- Estimate the mean: ______
- Estimate the SE (Standard Error): ______
**c. Sample Analysis:**
- **Scenario:** Random sample of 150 freshmen this fall; 82 were proficient.
- **Tasks:**
- Compute \( \hat{p} \) and locate it on the sampling distribution.
- Shade the area representing the extreme if this fall’s proficiency is 45%.
**d. Conclusion:**
- **Choose the Correct Words:**
- Your sample result **IS / IS NOT** consistent with a population percentage of 45%.
- You **DO / DON'T** have statistically significant evidence that this fall's percentage is different from 45%.
- If surveying all this fall’s freshmen, it **IS / IS NOT** plausible that 45% were proficient in math.
**Questions for Consideration:**
- If the null is true, is 50% proficiency in a sample unusual? ______ Explain:
- If the null is true, is having 45 proficient freshmen in your sample unusual? ______ Explain:
*Document Date: 7/18/20*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfc1f11b-dd1d-4452-af2e-391c3b670477%2Fc61f029b-4d3d-428f-b05e-6a1c6c9c020a%2Fjcayja_processed.jpeg&w=3840&q=75)
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