Year 1 Hypothesis Testing

Question 1

null hypothesis

Answer 1

Assume is correct
H0 = insert probability

Question 2

alternative hypothesis

Answer 2

Assume is wrong
H1 > / < / not equal to insert probability

Question 3

test statistic

Answer 3

value calculated from sample

Question 4

finding a critical value

Answer 4

actual significance = test statistic if it falls into the critical region

Question 5

set up for 1 tailed tests answer example:
Doctor suggests new drug is improvement of 11/20 score of old drug
5% significance

Answer 5

Define X variable
define p
X ~ B(20, p)
H0: p = 0.4 H1: p > 0.4
Assume H0 is true, so X ~ B(20, 0.4)
P(X >_ 11) = 1- P(X_<10) = 0.1275
0.1275 > 0.05 (test statistic > SL)
Not enough evidence to reject H0
concluding statement: new drug is not better than old one

OR VIA COMPARISON TO CRITICAL REGION

Question 6

set up for 2 tailed tests answer

Question 7

set up for 1 tailed critical value answer at 5% significance

Answer 7

Assume H0 is true, X ~ B(6,0.35)
P(X>4) = 1 - P(X<3) = 0.1174
P(X>5) = 1 - P(X<4) = 0.0223
0.0223 < 0.05 (test statistic < cv)
critical region is X>_5
Actual significance = 0.0223

Question 8

set up for 2 tailed critical value answer at 2% significance (close as possible to 0.01)

Answer 8

Assume H0 is true, X ~ B(4,0.25)
Lower tail:
P(X_<4) = 0.0160
P(X_<3) = 0.0047
0.0047 < 0.01 so CR is X<3
Upper tail:
P(X>18) = 1 - P(X<17) = 0.0047
P(X>17) = 1 - P(X<16) = 0.0116
0.0116 closes so CR X>17
CRITICAL REGIONS: X<3 & X>17
actual significance = 0.0116 + 0.0047