Question

1. Find the critical z-value(s) for a right-tailed test with α = 0.02Assume a normal population.

2. Find the critical t-value(s) for a two-tailed test with n = 12,  α = 0.05. Assume a normal distribution.

3. Express the claim in symbolic form: At least half the students at this school carpool to campus.

4. Express the claim in symbolic form:The average number of sick days taken annually by individual faculty members at this school is 4.

5. Express the claim in symbolic form: The mean annual rainfall for this county is no more than 42".

6. Express the claim in symbolic form: More than 25% of the injuries caused by fireworks occur to hands.

7. Convert the claim into a null hypothesis and an alternative hypothesis: p = 0.45

  H 0:

H 1:

8. Convert the claim into a null hypothesis and an alternative hypothesis: μ > 12

  H 0:

H 1:

9. Find the p-value for the test statistic z = 1.76 in a left-tailed test.

10. Find the p-value for the test statistic z = - 0.57 in a two-tailed test.

Answer 1

1)

From Z table,

Critical z value at 0.02 level = 2.054

2)

From T table,

t critical value at 0.05 level with 11 df = 2.201

3)

p > 0.5

4)

= 4

5)

< 42

6)

p > 0.25

7)

H0: p = 0.45

HA: p 0.45

8)

H0: <= 12

Ha: > 12

9)

p-value = P(Z < z)

= P(Z < 1.76)

0.9608

10)

p-value = 2 * P(Z < -0.57)

= 2 * 0.2843

= 0.5686