Question

State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results (make the appropriate statement of the results of the claim included rejection or non-rejection of the null hypothesis). Solve WITHOUT the use of P value. Please show all of your work.

A researcher wishes to see if students show a time preference for anatomy labs. A sample of four lab classes shows the enrollment. At a=0.10, do the students show a time preference for the labs?

	8 AM	12PM	2PM	4PM
Students	27	33	38	24

Answer 1

As we are testing here whether the students show a time preference for anatomy labs, therefore this is a chi square test for testing whether the distribution is uniform across the 4 time slots here.

The expected frequency here for each time slot here is computed as:
= (27 + 33 + 38 + 24) /4

= 30.5

Therefore the chi square test statistic here is computed as:

$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$

2 -Σ 3.52 + 2.52 + 7.52 + 6.52 305 = 3.84

For k - 1 = 3 degrees of freedom, we have from chi square distribution tables here:

$P(\chi^2_3 > 6.2514) = 0.1$

As the test statistic value here is 3.84 < 6.25 which is the critical value here, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here to show that the students show a time preference for anatomy labs