The side effects of a new drug are being tested against a placebo. A simple random sample of 565 patients yields the results below. At a significance level of ?? = 0.10, is there enough evidence to conclude that the treatment is independent of the side effect of nausea? Result
Drug
Placebo
Total
Nausea
36
13
49
No nausea
254
262
516
Total
290
275
565
The null hypothesis ??0:
The alternative hypothesis ????:
The level of significance ?? =
The degrees of freedom:
The test statistic:
The critical value:
Decision:
Answers
Answer:
There is enough evidence to conclude that the treatment is dependent to the side effect of nausea
Step-by-step explanation:
First we get the observed values, the observed values are the given.
Result Drug Placebo Total
Nausea 36 13 49
No Nausea 254 262 516
Total 290 275 565
Second Step is to get the expected Value
To get the expected value we need to multiply the row total to the column total and to divide it to the over all total
For Eg: we want to get the Drug Nausea of 36.
get the row total of Nausea which is 49
multiply it to total of column total of Drug which is 290 and divide it to the overall total which is 565
now we get the answer of 25.150442
Simply repeat this process.
getting the result of :
EXPECTED
DRUG PLACEBO
NAUSEA 25.150442 23.849558
NO NAUSEA 264.849558 251.150442
Third Step is to use the test statistic formula
which is = ∑((observed-expected)^2)/expected = ∑(O-E^2)/E
Now we simply apply it
For Eg: (36-25.150442)^2/25.150448 = 4.80351
Repeat the process for the other values
getting the result of :
DRUG PLACEBO
NAUSEA 4.680351 4.935643
NO NAUSEA 0.444452 0.468695
and add all to get the calculated value which is: 10.52914
Now we use the chi square graph to get the crit Value.
To get the crit Value we first get the degrees of freedom(df)
The formula for (df) is (number of rows -1) x (number of columns)
Now substitute (2-1)x(2-1) = 1, therefore our (df) is 1
Now we look for our significant value which is: 0.10, provided by the given
and look for (df) which is 1
we get the result of = 2.71
therefore our crit Value is 2.71
Lastly we compare our statistic value to crit value
if (calculated value>crit Value) we reject Null hypothesis and accept Alt hypothesis
if (calculated value<crit Value) we accept Null hypothesis and reject Alt hypothesis
Our given is that if Null Hypothesis = is that two variables are independent
and Alt Hypothesis = is that the two variables are dependent
Given that (10.52914>2.71) we reject Null Hypothesis and Accept Alt Hypothesis
Thus there is enough evidence to conclude that the treatment is dependent to the side effect of Nausea
a. The null hypothesis = the two variables are independent.
b. The alternate hypothesis = the two variables are dependent.
c. The level of significance = 0.10
d. The degrees of freedom = (number of rows = 2-1), (number of columns =2-1) = rows x columns = 1
e. The test statistic = ∑((observed-expected)^2)/expected = ∑(O-E^2)/E = 10.529
f. The critical value = using the chi square table with the row of significant value of 0.10 and column of df = 2.71
g. Decision = Since our x2>Crit Value. We reject the null hypothesis and accept the alternate hypothesis. Therefore, there is enough evidence to conclude that the treatment is dependent to the side effect of Nausea.
Answer:
Step-by-step explanation:
The null hypothesis ??0: the two variables are independent.
The alternative hypothesis ????: The treatment and responses have an adverse relationship with each other.
The level of significance ?? = 0.10
The degrees of freedom: 1 (one)
The test statistic: 10.53
The critical value: 2.706
Decision: . We reject the null hypothesis and accept the alternate hypothesis. Therefore, there is enough evidence to conclude that the treatment is dependent to the side effect of Nausea with the critical value of 2.706.
thank you!