The State of Pennsylvania has changed one of its toll roads from manual collection of tolls to machine collection. The idea behind the change was to allow traffic to flow more quickly through the toll plaza. With human attendants, the mean number of cars passing through the toll plaza was 1253 per hour with a standard deviation of 59. A random sample of 120 hours under the new machine system of toll collection shows a sample mean of 1261. Using the seven steps in significance testing, determine whether there is a statistically significant difference between the two systems such that more cars pass through with the new system. Show all seven steps. Should Pennsylvania adopt the new system for all toll roads in the state? Officials from Pennsylvania Department of Transportation (PENNDOT) question how a sample of 120 hours can prove whether or not more cars pass through with machine collections over manual collection, that is, how the results from the sample reflect the population. In a detailed paragraph of at least six to seven sentences, based on your knowledge and understanding of the concepts of inferential statistics, random sampling, and tests of statistical significance, respond to PENNDOT. Ensure that you mention what inferential statistics is and why we use it, what random sampling is, and what statistical significance is and why we test for it.

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Description: The State of Pennsylvania has changed one of its toll roads from manual collection of tolls to machine collection. The idea behind the change was to allow traffic to flow more quickly through the toll plaza. With human attendants, the mean number o

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The State of Pennsylvania has changed one of its toll roads from manual collection of tolls to machine collection. The idea behind the change was to allow traffic to flow more quickly through the toll plaza. With human attendants, the mean number of cars passing through the toll plaza was 1253 per hour with a standard deviation of 59. A random sample of 120 hours under the new machine system of toll collection shows a sample mean of 1261.

Using the seven steps in significance testing, determine whether there is a statistically significant difference between the two systems such that more cars pass through with the new system. Show all seven steps. Should Pennsylvania adopt the new system for all toll roads in the state?
Officials from Pennsylvania Department of Transportation (PENNDOT) question how a sample of 120 hours can prove whether or not more cars pass through with machine collections over manual collection, that is, how the results from the sample reflect the population. In a detailed paragraph of at least six to seven sentences, based on your knowledge and understanding of the concepts of inferential statistics, random sampling, and tests of statistical significance, respond to PENNDOT. Ensure that you mention what inferential statistics is and why we use it, what random sampling is, and what statistical significance is and why we test for it.

Statistics that allow for inferences or estimates about the population. Inferential statistics enable analysts come to conclusions about the population based on sample data. Inferential statistics cover the basics of inferential statistics, all kinds of hypotheses tests and their confidence intervals, design of experiments, and statistical power and errors. It also includes point estimation techniques, limit theorems, sampling distributions, approximations, and bounds. Correlation, regression, and association are also covered under inferential statistics to infer relationships between variables.

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