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1. For a sample of 100 employees, a personnel direc- tor has collected data on x 5 the number of years an employee has been with the firm and y 5 the number of shares of company stock the employee owns. The data are in file XR02044.
a. Generate a scatter diagram that includes the best-fit linear equation for these data.
b. Does there appear to be any relationship between the variables? If so, is the relationship direct or inverse?
c. Interpret the slope of the equation generated in part (a).
d. Viewing the scatter diagram and equation in part (a), do you think there are any employees who appear to own an unusually high or low amount of stock com- pared to the ownership that the equation would have predicted?
If f is upper semicontinuous on a compact space S, show that for some t ∈ S, f (t ) = sup f := sup{ f (x ): x ∈ S}. Hint: Let an ∈ R, an ↑ sup f . Consider f -1((-∞, an )), n = 1, 2,... .
Would it be unusual for a return with income of $100,000 or more to be audited? What is the probability that two randomly selected returns with income of $100,000 or more will not be audited?
A recent study stated that if a person chewed gum, the average number of sticks of gum he or she chewed daily was 8. To test the claim, a researcher selected a random sample of 36 gum chewers and found the mean number of sticks of gum chewed per d..
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
In baseball, a "no-hitter" is a regulation 9-inning game in which the pitcher yields no hits to the opposing batters. Chance (Summer, 1994) reported on a study of no-hitters in Major League Baseball (MLB).
Using the Hypothesis Tests Two Sample file and a .05 significance level, test whether there is a difference in the mean salary for men versus women.
Compute the pdf of continuous random variable Z where Z = X + Y and X is a continuous random variable uniformly distributed on [0, 2] and Y is a continuous random variable uniformly distributed on [0, 4]. Assume that X and Y are independent.
The standard deviation is thought to be $750. How many card holders should be sampled? Your company charges a set dollar amount for each account in the sample.
the amount of time spent watching television or playing video games is considered a significant factor on predicting
How many different combinations of the clients could be considered for inclusion into his limited schedule for that day?
The lifetime of a color television picture tube is normally distributed with a mean of 7.8 years and a standard deviation of 3 years. What is the probability that a picture tube will last more than ten years?
What sample size would be necessary to estimate the true weight with an error of +/- 0.03 grams with 90 percent confidence?
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