Rev Ch 10 Student by lzS2hR6Q

VIEWS: 69 PAGES: 4

									REVIEW CHAPTER 10


1.   A random sample of 85 students in Chicago city high schools take a course designed
     to improve SAT scores. Based on these students, a 90% confidence interval for the
     mean improvement in SAT scores for all Chicago city high school students is
     computed as (72.3, 91.4) points. The correct interpretation of this interval is

     (a)   90% of the students in the sample improved their scores by between 72.3 and
           91.4 points
     (b)   90% of the students in the population should improve their scores by between
           72.3 and 91.4 points
     (c)   None of the above


2.   Crop researchers plant 100 plots with a new variety of corn. The average yield for
     these plots is x = 130 bushels per acre. Assume that the yield per acre for the new
     variety of corn follows a normal distribution with unknown mean u and standard
     deviation  = 10 bushels per acre. A 90% confidence interval for  is

     (a)   130  1.645.
     (b)   130  1.96.
     (c)   130  16.45.


3.   A random sample is collected of size n from a population with standard deviation 
     and with the data collected a 95% confidence interval is computed for the mean of the
     population. Which of the following would produce a new confidence interval with
     smaller width (smaller margin of error) based on these same data?

     (a)   Increase .
     (b)   Use a smaller confidence level.
     (c)   Use a smaller sample size.


4.   To assess the accuracy of a kitchen scale a standard weight known to weigh 1 gram is
     weighed a total of n times and the mean, x , of the weighings is computed. Suppose
     the scale readings are normally distributed with unknown mean, m, and standard
     deviation  = 0.01 g. How large should n be so that a 90% confidence interval for m
     has a margin of error of  0.0001?

     (a)   165
     (b)   27061
     (c)   38416


                                                                                  Feb 2005
Rev Ch 10 p. 2


5.    The times for untrained rats to run a standard maze has a N (65, 15) distribution
      where the times are measured in seconds. The researchers hope to show that
      training improves the times. The alternative hypothesis is

      (a)    H a :   65.
      (b)    H a : x  65.
      (c)    H a :   65.


6.    A social psychologists reports that “in our sample, ethnocentrism was significantly
      higher (P  0.05) among church attendees than among non-attendees.” This means

      (a)   ethnocentrism was a least 5% higher among church attendees than among non-
            attendees.
      (b)   the observed differences between church attendees and non-attendees account
            for all but 5% of those sampled. These results are quite meaningful and should
            be investigated further
      (c)   if there is actually no difference in ethnocentrism between the church attendees
            and non-attendees, the chance that we would observe a difference as large or
            larger than we did is less than 5%


7.    The distribution of times that a company’s service technicians take to respond to
      trouble calls is normal with mean  and standard deviation  = 0.25 hours. The
      company advertises that its service technicians take an average of no more than 2
      hours to respond to trouble calls from customers.

      From a random sample of 25 trouble calls, the average time service technicians took to
      respond was 2.10 hours. How strong is the evidence against the companies claim?
      Based on these data, the P – value of the appropriate test is

      (a)   less than 0.0002.
      (b)   0.0228.
      (c)   0.0456.


8.    Suppose we are testing the null hypothesis H 0 :  = 50 and the alternative H a :   50
      for a normal population with  = 6. The 95% confidence interval for the mean is
      (51.3, 54.7). Then

      (a)   the P – value for the test is greater than 0.05.
      (b)   the P – value for the test is less than 0.05.
      (c)   the P – value for the test could be greater or less than 0.05. It can’t be
            determined without knowing the sample size.
Ch 10 p. 3


9.    Suppose that the population of the scores of all high school seniors that took the SAT-
      V (SAT verbal) test this year follows a normal distribution with mean  = 480 and
      standard deviation  = 90. A report claims that 10,000 students who took part in a
      national program for improving one’s SAT-V score had significantly better scores (at
      the 0.05 level of significance) than the population as a whole. In order to determine if
      the improvement is of practical significance one should

      (a)    find out the actual mean score of the 10,000 students.
      (b)    find out the actual P – value
      (c)    use a two-sided test rather than the one-sided test implied by the report.


10.   Does taking garlic tablets twice a day provide significant health benefits? To
      investigate this issue, a researcher conducted a study of 50 adult subjects who took
      garlic tablets twice a day for a period of six month At the end of the study, 100
      variables related to the health of the subjects were measured on each subject and the
      means compared to known means for these variables in the population of all adults.
      Four of these variables were significantly better (in the sense of statistical significance
      at the 5% level for the group taking the garlic tables as compared to population as a
      whole, and one variable was significantly better at the 1% level for the group taking the
      garlic tablets as compared to the population as a whole. It would be correct to
      conclude

      (a)    there is good statistical evidence that taking garlic tablets twice a day provides
             some health benefits.
      (b)    there is good statistical evidence that taking garlic tablets twice a day provides
             benefits for the variable that was significant at the 1% level. We should be
             somewhat cautious about making claims for the variables that were significant at
             the 5% level.
      (c)    None of the above.
Rev Ch 10 p. 4


11.   A significance test was performed to test the null hypothesis H 0 :  = 5 verses the
      alternative H a :   5. The test statistic is z = 1.5. The alpha level is .05. the P – value
      for this test is approximately ___.


12.   A local chamber of commerce claims that the mean family income level in a city is
      $12,250. An economist runs a hypothesis tests, using a sample of 135 families, and
      finds a mean of $11,500 with a standard deviation of $3180. Should the $12,250 claim
      be rejected at a 5% level of significance? Test the hypothesis that the mean family
      income is $12,250.


13.   Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district.


114 100 104        89   102 91 114 114 103 105 108 130 120 132 111 128
118 119 86         72   111 103 74 112 107 103 98   96 112 112 93

      Treat the 31 girls as an SRS of all seventh-grade girls in the school district. Suppose
      that the standard deviation of IQ scores in this population is known to be  = 15.

      a)    Give a 95% confidence interval for the mean IQ score  in the population.
      b)    Is there significant evidence at the 5% level that the mean IQ score in the
            population differs from 100? Give appropriate statistical evidence to support
            your conclusion.
      c)    In fact, the scores are those of all seventh-grade girls in one of the several
            schools in the district. Explain carefully why your results from (a) and (b) cannot
            be trusted.

								
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