In a particular year, 68% of online courses taught at a system of community colleges were taught by full-time faculty. To test if 68% also represents a particular state's percent for full-time faculty teaching the online classes, a particular community college from that state was randomly selected for comparison. In that same year, 35 of the 44 online courses at this particular community college were taught by full-time faculty. Conduct a hypothesis test at the 5% level to determine if 68% represents the state in question. Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part 1) Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.) The image depicts a bell-shaped curve, representing a normal distribution, which is used to illustrate a 95% confidence interval (C.I.).**Description of the Diagram:**- **Bell Curve:** The curve shown is symmetrical and centered, characteristic of a normal distribution.- **Shaded Area (95% C.I.):** The central part of the curve is shaded, indicating that 95% of the data falls within this interval. This area under the curve represents the range within which the true population parameter is expected to lie with 95% confidence.- **Tails of the Curve:** The unshaded areas on both ends of the curve are the tails, each containing 2.5% of the data, summing up to the remaining 5%.- **Markers on the X-axis:** The horizontal line below the curve has two vertical markers at the edges of the shaded area, representing the boundaries of the 95% confidence interval.In summary, this diagram visually represents how a 95% confidence interval captures the central portion of a normally distributed dataset.

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Description: In a particular year, 68% of online courses taught at a system of community colleges were taught by full-time faculty. To test if 68% also represents a particular state's percent for full-time faculty teaching the online classes, a particular communi

Given 68% of the online classes taught by full-time faculty A particular community was selected at…

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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In a particular year, 68% of online courses taught at a system of community colleges were taught by full-time faculty. To test if 68% also represents a particular state's percent for full-time faculty teaching the online classes, a particular community college from that state was randomly selected for comparison. In that same year, 35 of the 44 online courses at this particular community college were taught by full-time faculty. Conduct a hypothesis test at the 5% level to determine if 68% represents the state in question. Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part 1) Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.)

The image depicts a bell-shaped curve, representing a normal distribution, which is used to illustrate a 95% confidence interval (C.I.).

**Description of the Diagram:**

- **Bell Curve:** The curve shown is symmetrical and centered, characteristic of a normal distribution.
- **Shaded Area (95% C.I.):** The central part of the curve is shaded, indicating that 95% of the data falls within this interval. This area under the curve represents the range within which the true population parameter is expected to lie with 95% confidence.
- **Tails of the Curve:** The unshaded areas on both ends of the curve are the tails, each containing 2.5% of the data, summing up to the remaining 5%.
- **Markers on the X-axis:** The horizontal line below the curve has two vertical markers at the edges of the shaded area, representing the boundaries of the 95% confidence interval.

In summary, this diagram visually represents how a 95% confidence interval captures the central portion of a normally distributed dataset.

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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