# ) A lab is comparing a test drug to a standard drug that is use

August 30, 2017

Question
I) A lab is comparing a test drug to a standard drug that is useful to patients having high blood pressure. The standard therapy was administered to patients with comparable hypertension and the responses to therapy were classified into one of 4 response categories:
Marked decrease in blood pressure 50%
Moderate decrease in blood pressure 25
Slight decrease in blood pressure 10
Stationary 15
The lab then conducted a clinical trial with a random sample of 200 patients with high blood pressure on the test drug. Observed cell counts for the four categories were 120, 60, 10 and 10. Is this the same distribution as presented for the standard drug?
What test is appropriate for this problem?

State the null and alternate hypotheses

Find the expected cell counts

Find the test statistic

How many degrees of freedom will you use?

Find the critical value

Estimate the p-value. This is the probability of being more extreme (on the right side) then the test statistic.

II) Is there a relationship between the IQ of workers and their job performance? A sample of 400 cases
yielded the following results:

Intelligence

Below
Average
Average
Above
Average
Total

Poor
67

Fair
64

Good
25

42
10

76
23

56
37

Find the matrix of expected values:

What test is appropriate for this problem?

State the null and alternate hypotheses

Find the test statistic

How many degrees of freedom will you use?

Find the critical value

Total

3

Estimate the p-value

What is your conclusion at alpha = .10?

III) Samples of the members of five different labor unions were asked whether they are for or against a
certain piece of legislation:

For
Against

Union 1
74
26

Union 2
81
19

Union 3
69
31

Union 4
75
25

Union 5
91
9

Total

Use the 1% level of significance to test the null hypothesis that the corresponding true proportions are all
equal.

Find the matrix of expected values:

What test is appropriate for this problem?

State the null and alternate hypotheses

Find the test statistic

How many degrees of freedom will you use?

Find the critical value

Estimate the p-value

IV) The following is the gas mileages of 10 randomly selected cars, with and w/o a new gasoline additive
Does the gasoline additive improve gas mileage? Alpha = .05

Car
1
2
3
4
5
6
7
8
9
10

Gas mileage
25
20
28
18
19
12
29
8
23
10

Gas mileage
25
19
28
12
17
9
26
8
22
9

Difference
d

What test is appropriate for this problem?

State the null and alternate hypotheses

5

Find the critical value (s)

Find the test statistic

Estimate the p-value

If this test were two sided, testing whether mean mileage with and without additive is the same, at alpha = .10,
state the null and alternate hypotheses, draw the null distribution showing the critical values and find the
confidence interval for the mean difference in mileage with and without additive. Reach a conclusion using
this confidence interval and the hypothesized difference from your null hypothesis.

V) Does a dynamic system reduce the operative time relative to a static system. The following data on
operative times, in minutes, for the 2 systems is given. At the 1% significance level, does the data provide
sufficient evidence to conclude that the mean operative time is less with the dynamic system than with the
static system?
Dynamic
370
360
500
Static
430
445

510

445

295

315

455

455

490

490

345

450

505

335

280

535

What test are you going to use? Please justify your decision by conducting an F test at alpha= .20

325

Now please perform the appropriate comparison of means test
State the null and alternate hypotheses

Compute the degrees of freedom

Compute the test statistic

Find the critical value (s)

Estimate the p-value from the appropriate row of the t table

Draw a conclusion

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