Suppose that insurance companies did a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.Part 1) Which distribution should you use for this problem? (Round your answer to four decimal places.) P' ~ _____ (_____,_____)Part 2) Construct a 95% confidence interval for the population proportion who claim they always buckle up. (State the confidence interval, sketch the graph, and calculate the error bound) The image features a typical representation of a confidence interval in statistics. It includes a bell-shaped curve, likely representing a normal distribution.1. **Graph Elements**: - The horizontal line represents the range of possible values. - The curve in the center is a typical bell-shaped curve, indicative of a normal distribution. - There are vertical lines or arrows indicating the critical points on either side of the distribution curve.2. **Annotations**: - The text "α/2" appears twice, once at each end of the horizontal line. This represents the significance level split equally on both tails of the distribution. - "C.L.=" is centered above the curve, which stands for Confidence Level. This value indicates the probability that the parameter falls within the interval. - "P'" is located beneath the horizontal line, slightly off to the right. This could represent a point estimate or a particular value of interest on the distribution.This visualization is commonly used when explaining statistical confidence intervals, emphasizing the areas under the curve that fall within the desired confidence level and the tails associated with the significance level α.

From the given information, Consider, Sample size(n) =420 Proportion (p⏞) =0.8 Thus,

Answered: Suppose that insurance companies did a…

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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Suppose that insurance companies did a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.

Part 1) Which distribution should you use for this problem? (Round your answer to four decimal places.)

P' ~ _____ (_____,_____)

Part 2) Construct a 95% confidence interval for the population proportion who claim they always buckle up. (State the confidence interval, sketch the graph, and calculate the error bound)

The image features a typical representation of a confidence interval in statistics. It includes a bell-shaped curve, likely representing a normal distribution.

1. **Graph Elements**:
- The horizontal line represents the range of possible values.
- The curve in the center is a typical bell-shaped curve, indicative of a normal distribution.
- There are vertical lines or arrows indicating the critical points on either side of the distribution curve.

2. **Annotations**:
- The text "α/2" appears twice, once at each end of the horizontal line. This represents the significance level split equally on both tails of the distribution.
- "C.L.=" is centered above the curve, which stands for Confidence Level. This value indicates the probability that the parameter falls within the interval.
- "P'" is located beneath the horizontal line, slightly off to the right. This could represent a point estimate or a particular value of interest on the distribution.

This visualization is commonly used when explaining statistical confidence intervals, emphasizing the areas under the curve that fall within the desired confidence level and the tails associated with the significance level α.

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