The Percentage of Complete Passes Is an Important Measure for a Quarterback

question 56

Essay

The percentage of complete passes is an important measure for a quarterback in the NFL. A particular quarterback has a career completion percentage of 55%. The quarterback got a new coach and then played a few games where he completed 48 of 100 passes.
A) Specify the null and alternative hypotheses to determine whether the proportion of completed passes has decreased with the new coach.
B) Calculate the value of the test statistic and the p-value.
C) At the 5% significance level, can you conclude that the quarterback's completion percentage has decreased?

• A) Specify the null and alternative hypotheses to determine whether the proportion of completed passes has decreased with the new coach.
• B) Calculate the value of the test statistic and the p-value.
• C) At the 5% significance level, can you conclude that the quarterback's completion percentage has decreased?

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Definitions:

Population Distribution

The distribution of a characteristic within an entire population, described by parameters such as mean, variance, and standard deviation.

Null Hypothesis

A hypothesis that suggests there is no statistical significance between two variables, often used as a default hypothesis in testing.

Standard Deviation

A measure of the dispersion or spread of a set of values, indicating how much the values deviate from the mean of the data.

Test Statistic

A value calculated from sample data during a hypothesis test used to decide whether to reject the null hypothesis.