While conducting a goodness-of-fit test if the observed and expected values are close, you would expect which of the following? A. Large X2 value, large p-value
B. Small x2 value, large p-value
C. Large X2 value, small p-value
D. Small X2 value, small p-value

In this exercise we have to use probability knowledge so we can say that the correct alternative is:

Letter B

If the observed and expected values are close, then their differences are small leading to small squares of those differences. Consequently, this means the sum of the squared differences is also small leading to a small value.

The p-value is the probability of getting a certain chi-square value or larger. If  is small, then we have a very large chance of getting that certain value or larger. Visually, the area under the chi-square curve to the right of will be large if is small.

A large p-value means we fail to reject the null hypothesis. You can think of the p-value as the probability that the null is correct . This means a large p-value tells us to accept that the data fits the distribution we're trying to compare to.

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Choice B

Small X^2 value, large p-value

Explanation:

The X^2 refers to chi-squared or chi-square value.

If the observed and expected values are close, then their differences are small leading to small squares of those differences. Consequently, this means the sum of the squared differences is also small leading to a small X^2 value.

The p-value is the probability of getting a certain chi-square value or larger. If X^2 is small, then we have a very large chance of getting that certain X^2 value or larger. Visually, the area under the chi-square curve to the right of X^2 will be large if X^2 is small.

A large p-value means we fail to reject the null hypothesis. You can think of the p-value as the probability that the null is correct (though because of some technical reasons it's not this entirely, but its close enough). This means a large p-value tells us to accept that the data fits the distribution we're trying to compare to.

50- 250 is correct i did that one too

step-by-step explanation: