Week8 livelecture2010

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Summary of things you should know for the final exam.

Transcript of Week8 livelecture2010

  • 1. B Heard
    Lecture for the Final ExamStatistics For Decision Making
    Not to be used, posted, etc. without my expressed permission.B Heard

2. The final exam is cumulative.
It should take you around the full amount of time given.
Make sure you check the number of pages, etc. before starting.
Two Pages with 17 MC and 8 essay type problems
Final Exam Review
Not to be used, posted, etc. without my expressed permission.B Heard
3. Final Exam Review
What you should know.
Not to be used, posted, etc. without my expressed permission.B Heard
4. Know basic terms like mean, median, mode, standard deviation, variance, etc.
5. Be able to understand the normal distribution and how it relates to the mean, standard deviation, variance, etc.
For example, I did an analysis and found the mean number of failures was 7 and the standard deviation was 1.5. Answer the two questions below.
How many standard deviations is 10 from the mean?10 7 = 3, 3/1.5 = 2 (your answer)
How many standard deviations is 6.25 from the mean? 6.25 7 =- .75,- .75/1.5 = -0.5 (your answer)
Final Exam Review
6. Be able to use the Standard Normal Distribution Tables or
Excel to find probability values and z scores.
Examples:
Find the following probability involving the Standard Normal Distribution. What is P(z -.60)?
1 0.2743 =0.7257(using table or Excel 1 =NORMDIST(-0.6,0,1,TRUE))
Final Exam Review
7. Be able to find the probability that z is less than, greater than, or between two values
Remember you can do this using the Normal Distribution template using 0 (zero) as the mean and 1 as the standard deviation.
8. A researcher is performing a hypothesis teston a claim about a population proportion. Usingan alpha = .04 and n = 80, what is the rejection region if the alternate hypothesisis Ha: p > 0.70?
Alternate hypothesis test shows that this is a Right
Tailed test (since its p > 0.70) with a right tail area of .04
(since alpha = .04).Therefore we are going to reject Ho
if z > 1.75 (looked in standard normal table to find z
score for a probability of 0.96, z of 1.75 was the closest)
Final Exam Review
9. A researcher is performing a hypothesis teston a claim about a population proportion. Usingan alpha = .03 and n = 95, what two critical values determine the rejection regionif the null hypothesis is: Ho: p = 0.44?
Since Ho: p = 0.44, this is a two tailed test. Each tail has
an area = .03/2 = .015. The z-values that correspond to
this area in the tail is +/- 2.17. (You can see this by
finding the z score for either .015 or .985 realizing its two
tailed)
Final Exam Review
10. A manufacturer claims that the mean lifetime of its computer component is 1100 hours. A buyers researcher selects 49 of these components and finds the mean lifetime to be 1105 hours with a standard deviation of 30 hours. Test the manufacturer's claim. Use alpha = .02.
Answer on following chart
Final Exam Review
11. Ho: mu = 1100 hours (claim);
Ha: mu does not = 1100 hours; two tailed test, therefore, .01 is in left tail
and .01 is in right tail; thus critical values are 2.33;
test statistic is
z = (xbar - mu) [sigma sqrt(n)] = (1105 - 1100) [30 sqrt(49)] = 5 [30 7] = 5 4.29 = 1.17which is in the do not reject area because p value corresponding to z= +1.17 is 0.879
Fail toreject Ho. (Because 1.17 is in the bounds of the critical values
2.33)There is not enough evidence to reject the manufacturer's claim that
the mean lifetime is 1100 hours.
Final Exam Review
12. A Pizza Delivery Service claims thatit will get its pizzas delivered in less than 30 minutes. A random selection of 49 service times was collected, and their mean was calculated to be 28.6 minutes. The standard deviation was 4.7 minutes. Is there enough evidence to support the claim at alpha = .10. Perform an appropriate hypothesis test, showing each important step.(Note: 1st Step:WriteHo and Ha; 2nd Step: Determine Rejection Region; etc.)
Answer following chart
Final Exam Review
13. Ho: mu >= 30 min.
Ha: mu < 30 min. (claim). Therefore, it is a left-tailed test.
n=49; x-bar=28.6; s=4.7; alpha=0.10
Since alpha = 0.10, then the critical z value will be zc = -1.28
since n>30 then s can be used in place of sigma.
Standardized test statistic z = (x-bar - mu)/(s/sqrt(n)) z = (28.6-30)/(4.7/sqrt(49)) z = -2.085
since -2.085 < -1.28, we REJECT Ho.
That is, at alpha = 0.10, There is enough evidence to support the
Pizza Delivery Services claim.
(p-value method could have also been used)
Final Exam Review
14. Determine the minimum required sample size if you want to be 90% confident that the sample mean is within 5 units of the population mean given sigma = 8.4. Assume the population is normally distributed.
n = (Zc*sigma/E)^2 = [(1.645 * 8.4)/ 5]^2 = (2.7636)^2= 7.64= 8 (always round up sample sizes)
Final Exam Review
15. The failure times of a component are listed in hours. {100, 95, 120, 190, 200, 200,280}.Find the mean, median, mode, variance, and range.Do you think this sample might have come from a normal population? Why or why not?
mean = 169.3
median =190
mode = 200
variance = 4553.6
range = 185
Doubtful it came from a normal, compare mean, median,
mode, etc.
Final Exam Review
16. The random variable X represents the annualsalaries in dollarsfor a group of entry level accountants. Find the expected value E(X). X = {$30,000; $38,000; $42,000}. P(30,000) = .2; P(38,000) = .7; P(42,000) = .1

E(X) = 30000*.2 + 38000*.7 + 42000*.1 = $36,800
Final Exam Review
17. The average (mean) monthly grocery cost for a family of 4 is $600. The distribution is known to be normal with a standard deviation =60. A family is chosen at random. a) Find the probability that the familys monthly grocery cost purchases will be between $550 and $650.b)Find the probability that the familys monthly grocery cost purchases will be less than $700.c) What is the probability that the familys monthly grocery cost purchases will be more than$630?
Answers follow
Final Exam Review
18. Using Tables or EXCEL (I used an Excel Template like one I showed you):a) P(550 < x < 650) = 0.5953b) P(x < 700) =.9522 c) P(x > 630) = .3085
Final Exam Review
19. The earnings per share (in dollars) for The Very Pretty Products Company are given by the equation
y-hat = 0.863 + 0.029a - 0.011b
where "a" represents total revenue (in billions of dollars) and "b" represents total net worth (in billions of dollars). Predict the earnings per share when total revenue is $6 billionand net worth is $1 billion.

y-hat = 0.863 + 0.029a - 0.011b
y-hat = 0.863 + 0.029*6 - 0.011*1
y-hat = 1.026
Final Exam Review
20. The time required to produce a product was normally distributed with a mean10.5 days and a standard deviation of1.5 days (i.e., 36hours).What is the probability that it will take more that11days to produce the product?
We want P(X > 11)z = (x - mu)/sigma= (11 10.5)/1.5 = .5/1.5 = .33P(z > .33) = 1 - P(z < .33)= 1 0.6293= 0.3707
Final Exam Review
21. A shipment of 30 Widgits contains7 defective Widgits.How many ways can a Widget buying company buy3 of these units and receive no defective units?

There are 23 Widgets which are not defective.Thus there are 23C3ways to get3 sets of Widgets with none defective.23C3 = 1771 (using combin function in Excel)
Final Exam Review
22. For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made.A car manufacturer claims that the mean life time of a car is more than 7 years.

Ho: mu 7 years (claim)

Remember that Ho always contains equality and the claim can be either Ho or Ha
Final Exam Review
23. Know the difference between Binomial and Poisson
Remember we talked about this in a previous lecture!
24. A State Trooper notes that at a certain intersection, an average of three cars run the red-light per hour. What is the probability that the next time he is there exactly two cars run the red-light?

Poisson with average of 3. want P(2) P(2) = .2240(Use Excel or Excel Template)
Final Exam Review
25. The probability that a house in a neighborhood has a dog is 40%. If 50 houses in the neighborhood are randomly selected what is the probability thatone (or a certain number) of the houses will have a dog?

a.Is this a binomial experiment?

b. Use the correct formula to find the probability that, out of 50 houses, exactly 22 of the houses will have dogs. Show your calculations or explain how you found the probability.
Answer Follows
Final Exam Review
26. a) Fixed number of independent trials, only two possible outcomes in each trial {S,F} (dog or not), probability of success is the same for each trial, and random variable x counts the number of successful trials. So YES it is.

b) n = 50; p = .40 = P(success) = house has a dogWe want P(22) --> P(22) = .0959 (I used a Binomial Template)
Final Exam Review
27. Thestem and leaf plot for the following data is displayed below: {11,11,12,16,17,24,25,26,26,34,36,37,44,46,51,53,62}
Stem and Leaf Plot:1|112672|45663|4674|465|136|2
Discuss the shape of the data distribution.
It is right skewed. (other choices would be left skewed, symmetric, etc).This one is right skewed because if you turned it 90 degrees counter clockwise the tail would be on the right.
F