Question

Determine which distribution should be used in a hypothesis test with the following information, or if it is not appropriate to conduct a hypothesis test.

(a) The claim is μ

≤ 86. The sample data is: n = 29, ¯x

= 85.2, and s = 8. The population standard deviation is unknown, and the population is not even approximately normally distributed.

• Normal (z) distribution    (or Z-Test on the calculator)
• Student t distribution    (or T-Test on the calculator)
• A hypothesis test is not appropriate in this situation

(b) The claim is μ

= 64. The sample data is: n = 22, ¯x

= 61.9, and s = 7.8. The population standard deviation is known to be 5.8, and the population is normally distributed.

• Normal (z) distribution    (or Z-Test on the calculator)
• Student t distribution    (or T-Test on the calculator)
• A hypothesis test is not appropriate in this situation

Answer 1

(a) A hypothesis test is not appropriate in this situation.

(since population is not even approximately normally distributed. )

(b) Normal(z) distribution (or Z-test on the calculator)         

(since population standard deviation is known )