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Chapter 10: Q. AP3.10 (page 702)
Let X represent the outcome when a fair six-sided die is rolled. For this random variable, 渭X=and 蟽X=. If the die is rolled 100 times, what is the approximate probability that the sum is at least ?
a.
b.
c.
d.
e.
The probability is
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Each day I am getting better in math A "subliminal" message is below our threshold of awareness but may nonetheless influence us. Can subliminal messages help students learn math? A group of students who had failed the mathematics part of the City University of New York Skills Assessment Test agreed to participate in a study to find out. All received a daily subliminal message, flashed on a screen too rapidly to be consciously read. The treatment group of students (assigned at random) was exposed to "Each day I am getting better in math." The control group of students was exposed to a neutral message, "People are walking on the street." All students participated in a summer program designed to improve their math skills, and all took the assessment test again at the end of the program. The following table gives data on the subjects' scores before and after the program.
a. Explain why a two-sample t-test and not a paired t-test is the appropriate inference procedure in this setting.
b. The following boxplots display the differences in pretest and post-test scores for the students in the control (C) and treatment (T) groups. Write a few sentences comparing the performance of these two groups.
c. Do the data provide convincing evidence at the significance level that subliminal messages help students like the ones in this study learn math, on average?
d. Can we generalize these results to the population of all students who failed the mathematics part of the City University of New York Skills Assessment Test? Why or why not?
Literacy A researcher reports that of high school graduates, but only of high school dropouts, would pass a basic literacy test. Assume that the researcher鈥檚 claim is true. Suppose we give a basic literacy test to a random sample of high school graduates and a separate random sample of high school dropouts.be the sample proportions of graduates and dropouts, respectively, who pass the test.
a. What is the shape of the sampling distribution of . Why?
b. Find the mean of the sampling distribution.
c. Calculate and interpret the standard deviation of the sampling distribution.
A certain candy has different wrappers for various holidays. During Holiday , the candy wrappers are silver, red, and pink. During Holiday , the wrappers are silver and blue. In separate random samples of candies on Holiday and candies on Holiday , what are the mean and standard deviation of the total number of silver wrappers?
a.
b.
c.
d.
e.
A confidence interval for the proportion of the labor force that is unemployed in a certain city is Which of the following statements is true?
a. The probability is 0.96 that between of the labor force is unemployed.
b. About of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.
c. In repeated samples of the same size, there is a chance that the sample proportion will fall between
d. The true rate of unemployment in the labor force lies within this interval 96% of the time.
e. Between of the labor force is unemployed 96% of the time.
Artificial trees? An association of Christmas tree growers in Indiana wants to know if there is a difference in preference for natural trees between urban and rural households. So the association sponsored a survey of Indiana households that had a Christmas tree last year to find out. In a random sample of rural households, had a natural tree. In a separate random sample of urban households, had a natural tree. A confidence interval for the difference (Rural 鈥� Urban) in the true proportion of households in each population that had a natural tree is . Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.
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