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Chapter 9: Q 98. (page 610)

Music and mazes A researcher wishes to determine if people are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose previous research has established that the mean time needed for people to complete a certain maze (without music) is 40 seconds. The researcher decides to test the hypotheses H0:渭=40 versus Ha:渭<40 where 渭= the time in seconds to complete the maze while listening to classical music. To do so, the researcher has 10,000 people complete the maze with classical music playing. The mean time for these people is x=39.92 seconds, and the P-value of his significance test is 0.0002 Explain why this result is statistically significant, but not practically important.

Short Answer

Expert verified

Because the P-value is low, the result is static. Because a 0.08-second improvement is minor, the outcome is unimportant in practice.

Step by step solution

01

Given information

H0:渭=40H1:渭<40x=39.92P鈭�value=0.0002

02

Calculation

Assume that the level of significance 伪is 0.05

伪=0.05

Reject the null hypothesis H0if theP-value is less than the significance level, and the result is statistically significant.

0.0002<0.05鈬�Statisticallysignificant

However, the finding is not practically significant because the improvement was just 40-39.92=0.08 seconds, and 0.08 seconds is not a significant improvement in the maze completion time.

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Most popular questions from this chapter

18%Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1%increase in the sales tax to fund road repairs.

In the sample, p^=158/300=0.527, The resulting P-value is 0.18. What is the correct interpretation of this P-value?

a. Only 18% of the city residents support the tax increase.

b. There is an 18%chance that the majority of residents supports the tax increase.

c. Assuming that 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

d. Assuming that more than 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

e. Assuming that 50%of residents support the tax increase, there is an 18% chance that the null hypothesis is true by chance alone.

AttitudesThe Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' attitudes toward school and study habits. Scores range from 0 to 200 . Higher scores indicate better attitudes and study habits. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school, on average. She gives the SSHA to an SRS of 45 of the over 1000 students at her college who are at least 30 years of age.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

Walking to school Refer to Exercise 36.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100

Jump around Refer to Exercise 78.

a. Construct and interpret a 90% confidence interval for the true mean vertical jump 渭(in inches) of the students at Haley, Jeff, and Nathan鈥檚 school. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 78
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