Business Statistics Final Examination -
Question 1 - The owner of a company is concerned about absenteeism among his 100 workers and wishes to make an inference about the population mean daily number of workers absent. The number of present workers during the last 10-day pay periods are given in the following table:
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96
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99
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98
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98
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97
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98
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98
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100
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100
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96
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a. What is the best point estimate of the unknown population mean daily absent workers?
b. Construct and interpret a 98% confidence interval for the population mean.
c. Explain why the t distribution is used to calculate the confidence interval.
d. Is there significant evidence that during a typical pay period all workers are present?
Question 2 - According to a 2014 survey by the Pew Research Center the percentage of American adults who describe themselves as Christians was 70.6% in 2014, compared with 78.4% in 2007. The survey concludes that the Christian share of the U.S. population is declining. To test the validity of the research, a random sample of 51,891 adults in 2015 revealed 36,323 continue to identify themselves with some branch of the Christian faith.
a. With 99% confidence, conduct a test of hypothesis to determine whether the percentage of American adults who describe themselves as Christians decreased further in 2015.
b. What is the significance level?
c. Determine the level of significance that would have made the result of the test inconclusive. What is its name?
d. Calculate and interpret the value of β and show it graphically if the true population proportion of American adults who describe themselves as Christians is 69.8%.
Question 3 - The following are five pairs of observations of price, x, and quantity demanded, y:
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xi
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yi
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xi - x-
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(xi - x-)2
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yi - y-
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(yi - y-)2
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(xi-x-)(yi-y-)
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yi - y^i
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(yi - y^i)2
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1
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110
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2
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100
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3
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80
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4
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70
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5
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40
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Total
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a. Complete the above table.
b. Determine the regression equation.
c. Draw the scatter diagram of the five pairs of price/quantity and the regression line.
d. Interpret the values of the slope and y-intercept.
e. Estimate quantity demanded when price is $6.
f. Calculate and interpret the values of the coefficient of correlation and coefficient of determination.
g. Using a 95% confidence level, conduct a test of hypothesis to determine whether there is a linear relationship between the price and the quantity demanded.