Question

1. state whether the null hypothesis should be rejected on the basis of the given p - value. p - value = 0.0397, α = 0.10, two - tailed test

a) reject
b) do not reject

1. determine whether the outcome is a type i error, a type ii error, or a correct decision.

a correct decision of ( h_0: mu = 80 ) versus ( h_1: mu
eq 80 ). the true value of ( mu ) is 80 and ( h_0 ) is rejected.
a) type i error
b) type ii error
c) correct decision

1. which of the following would be classified as dependent samples?

i weights of identical twins
ii effects of a drug on tumor size of two different groups of people, measured by a before - and - after test
iii the effectiveness of two different brands of antacid on two different groups of people
iv the effectiveness of two different training programs on two different groups of individuals
v test scores of the same students in statistics and art
a) i, ii, iv
b) ii, v
c) i, ii, v
d) iii, iv

1. the football coach at state university wishes to determine if there is a change in offensive production between the first half and the second half of his teams recent games. the table below shows the first - half and second - half offensive production (measured in total yards gained per half) for the past six games.

game	1	2	3	4	5	6
second half yards	94	96	113	63	87	118

state the null and alternative hypotheses.
a) ( h_0: mu_d = 0; h_1: mu_d
eq 0 )
b) ( h_0: mu_d
eq 0; h_1: mu_d > 0 )
c) ( h_0: mu_d = 0; h_1: mu_d > 25.2 )
d) ( h_0: mu_d = 0; h_1: mu_d < 0 )

Explanation:

Question 16

Step1: Recall p - value rule

For a hypothesis test, if \( p - value<\alpha \), we reject the null hypothesis; if \( p - value\geq\alpha \), we do not reject the null hypothesis.

Step2: Compare p - value and α

Given \( p - value = 0.0397\) and \( \alpha=0.10 \). Since \( 0.0397<0.10 \), we reject the null hypothesis.

• Type I error: Rejecting \( H_0 \) when \( H_0 \) is true.
• Type II error: Failing to reject \( H_0 \) when \( H_0 \) is false.
• Correct decision: Reject \( H_0 \) when \( H_0 \) is false or fail to reject \( H_0 \) when \( H_0 \) is true.

Here, \( H_0:\mu = 80 \), \( H_1:\mu
eq80 \), true \( \mu = 80 \) (so \( H_0 \) is true) and \( H_0 \) is rejected. So this is a Type I error.

• Dependent samples: Samples where observations are paired (e.g., same individuals, related groups, before - after measurements).
• I: Weights of identical twins: Paired (related individuals) → dependent.
• II: Before - after test on the same group (even though it says two different groups, the before - after on each group makes it paired) → dependent.
• III: Two different brands on two different groups → independent.
• IV: Two different training programs on two different groups → independent.
• V: Test scores of same students in two subjects → paired (same students) → dependent.

So I, II, V are dependent.

Answer:

A) Reject

Question 17