Set 3.8: Hypothesis Testing and the z Score.

• Criterion: Evaluate a null hypothesis based on analysis of data.
• Data: Joan is 72 inches tall. The average (mean) height for adult women is 65 inches, and the standard deviation is 3.5 inches.
• Instructions:

a.State the null hypothesis. Population Mean=65 inches

b.State the alternative hypothesis. The alternative hypothesis is that the mean is higher than 65 inches.

c.Answer this: Joan is taller than what percentage of women in the population? (Hint: Think z score and area under the normal curve.)

(72-65)3.5=7=2z score=

3

=.9772

=98% Joan is taller than 97.7% of adult women

d.Answer this: Given Joan's height as compared to the population mean, do you expect to reject the null hypothesis? Explain your answer.

Yes, because the difference between two means is large enough that there is an uncertaintly that the mean is 65.

FEEDBACK-THE CRITERIA FOR THIS PROBLEM FIRST REQUIRES THE CALCULATION OF THE NORMAL DEVIATE Z. ONCE CALCULATED, IT IS NECESSARY TO UES THE GIVEN PORTION OF THE NORMAL CURVE IN ASSESSING THE VALUE.BE SURE TO INCLUDE THIS ASSESSMENT IN YOUR INTERPRETATION OF THE RESULTS.