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This question explores the concept of degrees of freedom. In statistics, the Binomial distribution with parameters N and p is the discrete probability distribution representing the number of successes in a sequence of N independent experiments. The resulting random variable X has possible integer values ranging from 0 to N. If N is known but p is not, we use the sample estimate p? = x?/N. A random sample of n = 300 observations has been drawn from a population of integer values ranging from 0 to N = 5. It produces the estimate p? = 0.482. Suppose we wish to perform a ?² goodness-of-fit test to see whether the population distribution is Binomial. Specifically, the null hypothesis states that the population distribution is binomial with N = 5 and p = 0.479. Answer the questions below, following clues you will find in the reading for this question (see the Test instructions). Note that f?, ..., f_N denote the frequencies of the values 0, ..., N in the sample. f? + f? + f? + f? + f? + f? = f? + 2f? + 3f? + 4f? + 5f? = Degrees-of-freedom of ?² test statistic:

          This question explores the concept of degrees of freedom. In statistics, the Binomial distribution with parameters N and p is the discrete probability distribution representing the number of successes in a sequence of N independent experiments. The resulting random variable X has possible integer values ranging from 0 to N. If N is known but p is not, we use the sample estimate p? = x?/N.
A random sample of n = 300 observations has been drawn from a population of integer values ranging from 0 to N = 5. It produces the estimate p? = 0.482.
Suppose we wish to perform a ?² goodness-of-fit test to see whether the population distribution is Binomial.
Specifically, the null hypothesis states that the population distribution is binomial with N = 5 and p = 0.479.
Answer the questions below, following clues you will find in the reading for this question (see the Test instructions). Note that f?, ..., f_N denote the frequencies of the values 0, ..., N in the sample.
f? + f? + f? + f? + f? + f? =
f? + 2f? + 3f? + 4f? + 5f? =
Degrees-of-freedom of ?² test statistic:

This question explores the concept of degrees of freedom. In statistics, the Binomial distribution with parameters N and p is the discrete probability distribution representing the number of successes in a sequence of N independent experiments. The resulting random variable X has possible integer values ranging from 0 to N. If N is known but p is not, we use the sample estimate p? = x?/N.
A random sample of n = 300 observations has been drawn from a population of integer values ranging from 0 to N = 5. It produces the estimate p? = 0.482.
Suppose we wish to perform a ?² goodness-of-fit test to see whether the population distribution is Binomial.
Specifically, the null hypothesis states that the population distribution is binomial with N = 5 and p = 0.479.
Answer the questions below, following clues you will find in the reading for this question (see the Test instructions). Note that f?, ..., fN denote the frequencies of the values 0, ..., N in the sample.
f? + f? + f? + f? + f? + f? =
f? + 2f? + 3f? + 4f? + 5f? =
Degrees-of-freedom of ?² test statistic:

Added by Andrea B.

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