# Mathematics

27)

 In a simple linear regression, the following information is given:
 = − 23; = 42;
 a. Calculate b1. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
 b1
 b. Calculate b0. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
 b0
 c-1. What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.)
 y-hat = + x
 c-2. Predict y if x equals −22.(Round intermediate coefficient values and final answer to 2 decimal places.)
 y-hat

28)

 Using data from 50 workers, a researcher estimates Wage = β0 + β1 Education + β2 Experience +β3 Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table.
 Coefficients Standard Error t Stat p-value Intercept 7.27 3.99 1.43 0.0629 Education 1.03 0.37 3.54 0.0001 Experience 0.43 0.11 3.23 0.0020 Age −0.01 0.06 −0.10 0.7920
a-1. What is the point estimate for β1?
 1.03 0.43
a-2. Interpret this value.
 As Education increases by 1 unit, Wage is predicted to increase by 1.03 units. As Education increases by 1 unit, Wage is predicted to increase by 0.43 units, holding Age and Experience constant. As Education increases by 1 unit, Wage is predicted to increase by 1.03 units, holding Age and Experience constant. As Education increases by 1 unit, Wage is predicted to increase by 0.43 units.
a-3. What is the point estimate for β2?
 0.43 1.03
a-4. Interpret this value.
 Same interpretation by using 1.03 or -0.01 As Experience increases by 1 unit, Wage is predicted to increase by 0.43 units, holding Age and Education constant.
 b. What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.)
 y-hat = + Education + Experience + Age
 c. What is the predicted value for Age = 38, Education = 3 and Experience = 5. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
 y-hat

29)

 Suppose that the average IQ score is normally distributed with a mean of 115 and a standard deviation of 11. In addition to providing the answer, state the relevant Excel commands. (Use Excel)
 a. What is the probability a randomly selected person will have an IQ score of less than 89? (Round your answer to 4 decimal places.)
 Probability
 b. What is the probability that a randomly selected person will have an IQ score greater than 125? (Round your answer to 4 decimal places.)
 Probability
 c. What minimum IQ score does a person have to achieve to be in the top 2.6% of IQ scores? (Round your answer to 2 decimal places.)
 Minimum IQ score

30)

 Consider the following frequency distribution.
 Class Frequency 2 up to 4 15 4 up to 6 65 6 up to 8 75 8 up to 10 15
 a. Calculate the population mean. (Round your answer to 2 decimal places.)
 Population mean
 b. Calculate the population variance and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)
 Population variance Population standard deviation

31)

 Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 15% of produced items are known to be nonconforming. Every week a batch of items is evaluated and the production machines are adjusted if the proportion of nonconforming items exceeds 19%. Use Table 1.
 a. What is the probability that the production machines will be adjusted if the batch consists of 68 items? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
 Probability
 b. What is the probability that the production machines will be adjusted if the batch consists of 136 items? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
 Probability

32)

 Assume that X is a binomial random variable with n = 27 and p = 0.92. Calculate the following probabilities. (Round your intermediate and final answers to 4 decimal places.)
 a. P(X = 26) b. P(X = 25) c. P(X ≥ 25)

33)

 A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individual’s annual salary in thousands of dollars:
 Education 3 4 6 2 5 4 8 0 Salary \$39 48 62 47 75 53 107 50 Click here for the Excel Data File

 a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.)
 + Education
b. Interpret the coefficient for education.
 As Education increases by 1 unit, an individual’s annual salary is predicted to increase by \$7,000. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by \$8,000. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by \$7,000. As Education inceases by 1 unit, an individual’s annual salary is predicted to decrease by \$8,000.
 c. What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)
 \$

34)

 A sample of patients arriving at Overbrook Hospital’s emergency room recorded the following body temperature readings over the weekend:
 99.0 100.4 99.7 100.4 99.1 101.7 100.9 100.5 99.3 101.9 100.4 101.9 100.5 99.4 102.7 99.4 100.9 100.1 100.7 100.2
 a. Construct a stem-and-leaf diagram.
 Stem Leaf
b. Interpret the stem-and-leaf diagram.
 The distribution is symmetric. The distribution is Positively Skewed. The distribution is Negatively Skewed.

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