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A wedding caterer randomly selected clients from the past few years and recorded the months in which the wedding receptions were held. She was interested in testing a claim that weddings occur in different months with the same frequency. She found the test statistic to be X squared equals 10.600. Use a 0.05 significance level to find the critical value for the goodness of fit and test the claim that weddings occur in different months with the same frequency than state the conclusion.


19.675; fail to reject the null hypothesis

21.026;reject the null hypothesis

21.026; fail to reject the null hypothesis

19.675; reject the null hypothesis

Sagot :

Lanuel

Based on a critical value of 21.026, we would fail to reject the null hypothesis because it's greater than the absolute value of the test statistic (10.600).

What is a critical value?

A critical value can be defined as a measurement which is used to calculate the margin of error that exists in a data set. Mathematically, it is expressed as follows:

Critical value (p*) = 1 - (α/2)

Critical value (p*) = 1 - (0.05/2)

Critical value (p*) = 1 - 0.025

Critical value (p*) = 0.975.

Also, the degrees of freedom (df) is given by:

Degrees of freedom (df) = n - 1

Degrees of freedom (df) = 13 - 1

Degrees of freedom (df) = 12.

From the Chi-square distribution table, a critical value at t₀.₀₅, ₁₂ = 21.026.

Note: If the critical value (21.026) is lesser than the absolute value of the test statistic (10.600), then we would reject the null hypothesis.

Read more on goodness-of-fit test here: https://brainly.com/question/16910222

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