Question

USE CALCULATOR AND SHOW FULL STEPS FOR EACH TEST INCLUDING WHAT YOU INPUT Below are random samples of enrollments for medical schools that specialize in research and for those that specialize in primary care. Is there a difference in the average enrollment for the two specializations? Use a significance level of a = 0.05.

a) Give the name of the hypothesis test that would be appropriate for this situation. (1 point)

b) State the hypotheses in symbols. (2 points)

c) Use your calculator to perform the appropriate hypothesis test and report the test statistic and p-value. Do not make these calculations by hand. Instead, use the correct command in your graphing calculator and write out what you entered. (3 points)

d) Make a sketch of the test distribution. Be sure to label the test statistic and p-value. (2 points)

e) Write a full conclusion for this test in the context of the problem. (2 points)

Research 474 577 605 783 467 670 414 813 443 565 696 277 419 884 663 692 694

Primary Care 783 605 427 728 546 474 371 107 442 587 293 277 662 555 527 320

Answer 1

a) Two sample t test will be used here for hypothesis testing.

b) The hypotheses are

c) Hypothesis testing by excel add onn

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	596.2352941	481.5
Variance	26646.06618	32182.8
Observations	17	16
Hypothesized Mean Difference	0
df	30
t Stat	1.917899527
P(T<=t) one-tail	0.032343507
t Critical one-tail	1.697260887
P(T<=t) two-tail	0.064687015
t Critical two-tail	2.042272456

the test statistic is

1.917899527

p-value is

0.064687015

Command used in calculator is shown below please enter the calculated values in calculator, iam showing with an example and with a snapshot.

d) The sketch for this distribution

e) Conclusion:

Since t statistics is less than t critical and p value is greater than alpha that is level of significance hence we fail to reject the null hypothesis and conclude that there is no significant difference in means.