Consider the following to answer the question(s) below:
A walk-in medical clinic believes that arrivals are equally distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.

-At α = 0.05,
A) we fail to reject the null hypothesis and conclude that arrivals are equally distributed based on this sample.
B) we reject the null hypothesis.
C) we fail to reject the alternative hypothesis and can conclude that arrivals are not equally distributed based on this sample.
D) we support the alternative hypothesis. There is strong evidence that arrivals are not the same over weekdays.
E) as the P-value = 0.645 is high, we conclude that arrivals are not equally distributed. Monday arrivals are the highest.

Question

Consider the following to answer the question(s) below:
A walk-in medical clinic believes that arrivals are equally distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
 
-At α = 0.05,
A) we fail to reject the null hypothesis and conclude that arrivals are equally distributed based on this sample. 
B) we reject the null hypothesis. 
C) we fail to reject the alternative hypothesis and can conclude that arrivals are not equally distributed based on this sample. 
D) we support the alternative hypothesis. There is strong evidence that arrivals are not the same over weekdays. 
E) as the P-value = 0.645 is high, we conclude that arrivals are not equally distributed. Monday arrivals are the highest.

Quizplus · Accepted Answer

We can test if arrivals are equally distributed over weekdays using a chi-squared goodness-of-fit test. The null hypothesis is that the observed frequencies match the expected frequencies (i.e., arrivals are equally distributed). The alternative hypothesis is that the observed frequencies do not match the expected frequencies (i.e., arrivals are not equally distributed).

Using the data given, we calculate a test statistic of 4.00 and a P-value of 0.406. At a significance level of 0.05, we fail to reject the null hypothesis (because the P-value is greater than 0.05) and conclude that arrivals are equally distributed based on this sample.

Therefore, the best choice is A.

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