Question

Isabel Myers was a pioneer in the study of personality types. In a random sample of 519 judges, it was found that 285 were introverts. Do the data indicate that a majority of judges are introverts? Use a = 0.05.

State the null and alternate

Do runners have lower heart rates, on average? Assume that non-runners have an average heart rate of 72 beats per minute.

1 State the null and alternate hypotheses.

What is the level of significance?

2. Suppose that we know that s =7 beats per minute. We randomly sample 50 runners and find that x =68.25 beats per minute. Find the test statistic. 3.Would it be likely to see x =68.25 (or less) if m =72? Explain.

. If we decide to “reject H0 ” could we be doing this in error?

Errors in hypothsesis testing If we reject H0 when it is, in fact, true, we have made a Type I error. If we accept H0 , when it is, in fact, false, we have made a Type II error. Note: A hypothesis test is statistically significant at the a level if P -value £a . That is, at the a level of risk, the evidence is sufficient to discredit H0 in favor of H1 . 5. Is this hypothesis test statistically significant?

  Testing the Mean m Steps to a hypothesis Test

1. State H0 , H1 and a .

2. Compute test statistic

3. Compute P -value

4. Make decision 5.

Write conclusion

High airline occupancy rates on scheduled flights are essential to corporate profitability. Suppose a scheduled flight must average at least 80% occupancy in order to be profitable and examination of the occupancy rate for fifty 7AM weekday flights from San Jose to Los Angeles showed a mean occupancy rate of 78%. Assume s = 6% . Does this indicate that the scheduled flight is unprofitable? Use a = 0.05.

Answer 1

(1)

Data:    

n = 519   

p = 0.5   

p' = 0.5491329   

Hypotheses:   

Ho: p ≤ 0.5   

Ha: p > 0.5   

Decision Rule:   

α = 0.05   

Critical z- score = 1.644853627

Reject Ho if z > 1.644853627

Test Statistic:   

SE = √ {(p (1 - p)/n} = √(0.5 * (1 - 0.5)/√519) = 0.021947564

z = (p' - p)/SE = (0.549132947976879 - 0.5)/0.0219475640653074 = 2.238651535

p- value = 0.0125893   

Decision (in terms of the hypotheses):

Since 2.2386515 > 1.644853627 we reject Ho

Conclusion (in terms of the problem):

It appears that a majority of the judges are introverts.