Question

Conduct a hypothesis test for each problem, using the traditional method. Show the 5 steps and all work for each hypothesis test. Be sure you select the correct test to use for each problem.

2. A college statistics instructor claims that the mean age of college statistics students is 25. A random sample of 98 college statistics students revealed a mean age of 23.1. The population standard deviation is known to be 3.21 years. Test his claim at the 0.05 level of significance.

3. A random sample of 113 adults ages 18-24 showed that 27 had donated blood within the past year, while a random sample of 166 adults who were at least 25 years old had 48 people who had donated blood within the past year. At the 0.10 level of significance, test the claim that the proportion of blood donors is equal for these two age groups.

Answer 1

Question 2

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


Z = -5.8595

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

There is insufficient evidence to support the claim that mean age of college statistic students is 25.

Question 3

To Test :-

H0 :- P1 = P2

H1 :- P1   P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 27 + 48 ) / ( 113 + 166 )
= 0.2688

Z = -0.93

Test Criteria :-
Reject null hypothesis if

= -0.93 > -1.64, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z < -0.93 )
P value = 0.3524
Reject null hypothesis if P value <
Since P value = 0.3524 > 0.1, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is sufficient evidence to support the claim that proportion of blood donor is equal.