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free/or 0.5$ |
| m464 | Fry Brothers Heating and Air Conditioning Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air-conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value? |
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| m465 | A function f: R2 -> R is said to be independent of the second variable if for each x € R we have f (x, y1) = f (x, y2) for all y1, y2. €R Show that f is independent of the second variable if and only if there is a function f: R->R such that f(x, y) = g(x). What is f1 (a, b) in terms of g1? |
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| m466 | A function f: Rn -> R is is homogeneous of degree m if f (tx) = tmf(x) for all x and t. If f is also differentiable, show that |
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| m467 | A function f: Rn x Rm-> Rp is bilinear if for x,x1, x2 € R n, y,y1, y2 € Rm and a € R
We have,
f(ax, y) = af (x, y) = f(x, ay)
f(x1 + x2, y) = f(x1, y) + f(x2, y)
f(x, y1 +y2) = f(x, y1) + f(x, y2)
(a) Prove that if f is bilinear, then
(b) Prove that Df (a, b) (x, y) = f (a,y) + f(x,b).
(c) (Show that the formula for Dp (a, b) in theorem 2-3 is a special case of (b |
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| m468 | f(x) = (3/4) (1/4)x , x = 0,1,2,...
(a) P (X = 2) (b) P (X < 2)
(c) P (X >2) (d) P (X > 1) |
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| m469 | Generalize the divergence theorem to the case of an -manifold with boundary in Rn. |
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| m470 | Generalize Theorem 5-6 to the case of an oriented (n - 1) -dimensional manifold in Rn.
The generalization is w Є A n-1(Mx) defined by |
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| m471 | Geoff Brown is the manager for a small telemarketing firm and is evaluating the sales rate of experienced workers in order to set minimum standards for new hires. During the past few weeks, he has recorded the number of successful calls per hour for the staff. These data appear next along with some summary statistics he worked out with a statistical software package. Geoff has been a student at the local community college and has heard of many different kinds of probability distributions (binomial, normal, hyper geometric, Poisson, etc.). Could you give Geoff some advice on which distribution to use to fit these data as well as possible and how to decide when a probationary employee should be accepted as having reached full production status? This is important because it means a pay raise for the employee, and there have been some probationary employees in the past who have quit because of discouragement that they would never meet the standard.
Successful sales calls per hour during the week of August 14:
Descriptive statistics:
Which distribution do you think Geoff should use for hisanalysis? |
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| m472 | GfK Custom Research North America conducted identical surveys 5 years apart. One question asked of women was “Are most men basically kind, gentle, and thoughtful?” The earlier survey revealed that, of the 3,000 women surveyed, 2,010 said that they were. The later revealed 1,530 of the 3,000 women surveyed thought that men were kind, gentle, and thoughtful. At the .05 level, can we conclude that women think men are less kind, gentle, and thoughtful in the later survey compared with the earlier one? |
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| m473 | Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor’s. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. For the Gibbs brand, the population standard deviation of the sample is 2.3 pounds. A sample of 55 babies using the competitor’s brand revealed a mean increase in weight of 8.1 pounds. The population standard deviation is 2.9 pounds. At the .05 significance level, can we conclude that babies using the Gibbs brand gained less weight? Compute the p-value and interpret it. |
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| m474 | Give an example of a bounded set C of measure 0 such that ∫ AXC does not exist. |
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| m475 | Given the following ANOVA table:
a. Determine the coefficient of determination.
b. Assuming a direct relationship between the variables, what is the correlation coefficient?
c. Determine the standard error ofestimate. |
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| m476 | Given the following hypotheses:
H0: µ = 10
H1: µ ≠10
A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis? |
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| m477 | Given the following hypotheses:
H0: µ ≤ 10
H1: µ > 10
A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level:
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis? |
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| m478 | Given the following hypotheses:
H0: µ = 100
H1: µ ≠ 100
A random sample of six resulted in the following values: 118, 105, 112, 119, 105, and 111. Assume a normal population. Using the .05 significance level, can we conclude the mean is different from 100?
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis?
d. Estimate the p-value. |
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| m479 | Given the following hypotheses:
H0: µ ≥20
H1: µ < 20
A random sample of five resulted in the following values: 18, 15, 12, 19, and 21. Assume a normal population. Using the .01 significance level, can we conclude the population mean is less than 20?
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis?
d. Estimate the p-value. |
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| m480 | Given the following regression output,
Answer the following questions:
a. Write the regression equation.
b. If x1 is 4 and x2 is 11, what is the expected or predicted value of the dependent variable?
c. How large is the sample? How many independent variables are there?
d. Conduct a global test of hypothesis to see if any of the set of regression coefficients could be different from 0. Use the .05 significance level. What is your conclusion?
e. Conduct a test of hypothesis for each independent variable. Use the .05 significance level. Which variable would you consider eliminating?
f. Outline a strategy for deleting independent variables in thiscase. |
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| m481 | Given the following sample of five observations, develop a scatter diagram, using x as the independent variable and y as the dependent variable, and compute the correlation coefficient. Does the relationship between the variables appear to be linear? Try squaring the x variable and then develop a scatter diagram and determine the correlation coefficient. Summarize youranalysis. |
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| m482 | Grand Strand Family Medical Center treats minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, one in the Little River Area and the other in Murrells Inlet. The Quality Assurance Department wishes to compare the mean waiting time for patients at the two locations. Samples of the waiting times for each location, reported in minutes, follow:
Assume the population standard deviations are not the same. At the .05 significance level, is there a difference in the mean waitingtime? |
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| m483 | Graph the number on the number line. |
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