Question

8. Researchers investigated the issue of race and equality of access to clinical trials. The table given in (a) shows the population distribution and the numbers of participants in clinical trials involving lung cancer At a significance level of 0.01, using a P-value test, test the claim that the distribution of clinical trial participants fits well with the population distribution. Is there a race/ethnic group that appears to be very underrepresented? Use the following steps: (a) Complete the expected column in the table below, use for E. Expected Expected Percentage (p)Frequency (0) Frequency (E)-np 756% 9.1% 10.8% Observed Race/ethnicity White(non-Hispanic) 3855 60 316 54 12 Black Asian/Pacific Islander American Indian/Alaskan Native 3.8% 0.7% n-4297 HINT: Asa double-check, add up the expected frequency column, it should also total n (within a small rounding error) (b) What is the name of the test we will be using and what is alpha? Test: (c) Write the equation that would be used to find the test statistic z and calculate the degrees of freedom. (d) Using technology, find X and P final answer] χ. [final answer] P- (e) What are the null and alternate hypotheses? Ho: H1: (f) Do you "reject" or "fail to reject" the null hypothesis? Why2 (show P-value test) (g) What is your conclusion about the original claim? (h) From comparing E and 0, which two groups in particular seem particularly underrepresented?

Answer 1

a).

race	expected percentage(p)	observed frequency	expected frequency(n*p)
white	75.6%	3855	4297*75.6%=3248.53
Hispanic	9.1%	60	4297*9.1%=391.03
black	10.8%	316	4297*10.8:%=464.08
Asian	3.8%	54	4297*3.8%=163.29
American Indian	0.7%	12	4297*0.7%=30.08
total	100%	n=4297	-------

b).name of test used:chi-squared test

  alpha=0.01

c).equation for test statistic:

(observed- expected) erpected

degrees of freedom:

number of response categories - 1 = 5-1 = 4

d).i have done the calculations in minitab. steps are -

copy race in one column,observed frequency in next column and expected proportions in another column $\rightarrow$stat $\rightarrow$tables $\rightarrow$chi-square goodness of fit test (one variable) $\rightarrow$ in observed counts enter observed counts $\rightarrow$ in category names enter race $\rightarrow$ under test,select specific proportions, and enter proportions. $\rightarrow$ok $\rightarrow$ok.

Observed and Expected Counts

Category	Observed	Test Proportion	Expected	Contribution to Chi-Square
w	3855	0.756	3248.53	113.221
h	60	0.091	391.03	280.234
b	316	0.108	464.08	47.248
a	54	0.038	163.29	73.144
ai	12	0.007	30.08	10.866

Chi-Square Test

N	DF	Chi-Sq	P-Value
4297	4	524.713	0.000

so our chi-square  = 524.713

p value =

Pl)-> 524.713) = 0.000

e).the null hypothesis must contain the condition of equality,so we have,

H0: p1=75.4/100, p2=9.1/100, p3=10.8/100, p4=3.8/100 and p5=0.7/100

H1: at least one of the proportion is not equal to the given claimed value.

here the null hypothesis is the claim.

f).here 0.000<0.01

so,here is enough evidence to reject the null hypothesis.

g)my conclusion about the original claim is:

.this goodness of fit test suggests that the distribution of clinical trial of participants do not fits well with the population distribution .

h).from comparing E and O ,

the Hispanic group(obs 60,exp 391.03) and the Asian(obs 54,exp 163.29) in particular seems particularly underrepresented.

***the calculation of chi-square statistic by hand is given below for further reference:

race	observed	expected	obs-exp	(obs-exp)^2	(obs-exp)^2/exp
white	3855	3248.53	606.47	367805.8609	113.2222
Hispanic	60	391.03	-331.03	109580.8609	280.2365
black	316	464.08	-148.08	21927.6864	47.2498
Asian	54	163.29	-109.29	11944.3041	73.1478
American Indian	12	30.08	-18.09	326.8864	10.8672
total	n=4297	-------	------	----	524.7235=$\chi ^2$