Question

Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead?

Answer 1

Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.

Given statement;

Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.

→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.

To learn more about binomial distribution click here:

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