1.         Parking Tickets – The Kaiserslautern police department claims that it issues an average of only 60 parking tickets per day.  The data below, reproduced in your Excel answer workbook,  show the number of parking tickets issued each day for a randomly selected period of 30 days.  Assume σ =13.42.   State the null and alternate hypotheses, as well as the claim, which (hint!) is in the null hypothesis.  Is there enough evidence to reject the group’s claim at  α = .05?   (As with all of these exercises, use the P-value method, rounding to 4 digits.)  (Hint:  so since we know the population standard deviation, use the standard normal distribution z-test .) (Monday class)

            79        78        71        72        69        71        57        60

            83        36        60        74        58        86        48        59

            70        66        64        68        52        67        67

            68        73        59        83        85        34        73

(Note:  You’ll find these data posted in Worksheet #1 of the Excel answer template.)

A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 60% chance of hiring at least two candidates. There is only a 7% chance that it will not make any hires and a 10% chance that it will make all three hires.

a. What is the probability that the firm will make at least one hire? (Round your answer to 2 decimal places.)

b. Find the expected value and the standard deviation of the number of hires. (Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.)

1. In a local agricultural reporting area, the average wheat yield is known to be 50 bushels

per acre with a wheat yield standard deviation of 10 bushels. The wheat yield is known to

be approximately normally distributed.

a) What percentage of the wheat yield is below 40 bushels per acre?

b) If a random sample of 25 acres is selected, what is the probability that the sample

mean yield will be between 48 and 52 bushels?

2. The weight of cans of sardines from a production line are normally distributed with a

mean of 16.8 oz and a variance of 2.25 oz. For each run of the process, 100 cans are

selected randomly and weighted. What is the probability that the average weight of these

cans is between 16.5 and 17.1 oz?

3. The Sullivan Advertising Agency has determined that the average cost to develop a 30-

second commercial is P50,000. The cost is assumed to be normal. What is the probability

that a random sample of 25 commercials with a standard deviation of P6,000 will have a

mean cost of P51,582 or less?

4. Two sets of bolts are intended to have different lengths but the same diameter. The

diameters of bolts of Type I have a variance of 4 cm; the diameters of the bolts of Type II

have a variance of 12 cm. Random samples of 10 bolts of Type I and 20 bolts of Type II

are obtained. What is the probability that the sample means will differ by at least 1.5 cm?

5. A random sample of 10 students from QUAMETH EA has an average grade of 65 with a

variance of 25; an independent random sample of 18 students from QUAMETH EB has

an average grade of 70 with a variance of 20. Assume that the grades of the two sections

are independently normally distributed with the same variance and means differing by 5

with the average of grade of EB higher than that of EA. Find the probability that the

sample mean of QUAMETH EB is at least 10 points higher than the sample mean of

QUAMETH EA.

6. Manufacturers of golf balls are concerned with a scientific concept called the coefficient

of restitution, defined as the ratio of the relative velocity of the ball and club after impact

to the relative velocity before impact. A manufacturer has developed a new solid-core

golf ball which he wishes to sell side-by-side with his firm's standard brand. The mean

coefficient of restitution for the new solid-core ball and the firm's standard brand of golf

ball are 0.69 and 0.55, respectively. The standard deviations of the coefficient of

restitution are 0.18 for the solid-core golf ball and 0.22 for the firm's standard brand. The

coefficient of restitution of the two types of golf balls can be assumed to be normally

distributed. A large institutional buyer of golf balls selects a random sample of 25 solid-

core golf balls and another random sample of 21 standard golf balls to test and compare

the two brands. Referring to the samples:

a) What is the probability that the mean coefficient of restitution of the solid-core golf

ball is greater than that of the standard golf ball?

b) What is the probability that the variance of coefficient of restitution of the solid-core

golf ball is less than 0.01674?

c) What is the probability that the ratio of the variance of the solid-core golf ball to the

standard brand is between 1.3924 and 1.9145?

7. The washers used in a particular type of motor are required to be of uniform thickness and

are manufactured so that the thickness has a standard deviation of a 0.0001 cm. What is

the probability that the standard deviation of a random sample of 25 washers is between

0.000072 cm and 0.00014 cm? Assume normality of population.

8. The variance of population 1 is twice the variance of population 2. Independent random

samples of size 16 and 11 are taken from these two normal populations. What is the

probability that the sample variance from population 1 is less than 5.7 times the sample

variance from population 2?

9. It is known that 5% of the radio tubes produced by a certain manufacturer are defective. If

the manufacturer sends out lots containing 100 tubes, what is the probability that at least

98% of the tubes are good?

10. The proportion of male births in the country per week is 0.48. What is the probability that

UST Hospital, which normally carries out natal deliveries at the rate of 40 babies per

week, will deviate at most 10% from the national statistic?

11. The proportion of households who watch a TV special in Ilocos is 60%. In Leyte, the

proportion of households who watch the same special is 70%. If a sample of 50 is

obtained from each province, what is the probability that the sample proportion from

Ilocos is less than that of Leyte?

12. A manufacturer produces test tubes from two independent processes. Process 1 produces

10% defectives while Process 2 produces 15% defectives. Random samples of size 100

are obtained from each process on a daily basis. What is the probability that the sample

from Process 1 has fewer defectives than the of Process 2?

13. A new process will be installed if its mean processing time is at most 20 minutes. The

new procedure was tried. In a random sample of 50 trials, an average processing time of

22.2 minutes with a standard deviation of 4.3 minutes was obtained. At a level of

significance of 0.05, should the new process be installed?

14. The output of a chemical process is monitored by taking a sample of 20 vials to determine

the level of impurities. The desired mean level of impurities is 0.040 grams per vial. If the

mean level of impurities in the sample is too high, the process will be stopped and

purged; if the sample mean is too low, the process will be stopped and the values will be

readjusted. Otherwise, the process will continue.

a) Sample results provide sample mean to be equal to 0.047 grams with sample standard

deviation equal to 0.018. At a significance level of 0.01, should the process be

stopped? If so, what type of remedial action will be required?

b) Assume that the mean level of impurities is within tolerable limits. If the maximum

tolerable variability of the process is 0.0002, do the sample results verify the

suspicion that the maximum tolerable variability has been exceeded? Use a 5% level

of significance.

15. Two astronomers recorded observations on a certain star. The 35 readings obtained by the

first astronomer have a mean reading of 1.45. The 32 observations by the second

astronomer have a mean reading of 1.30. Past experience has indicated that each

astronomer obtains readings with a variance of 0.50. Is there any difference between the

mean readings of the two astronomers? Use a level of significance of 0.01.

17. An advertising executive claims 50% of the people who saw Voltes V will remember the

name of their product after they watched the show. If 65 viewers in a random sample of

150 remembered the name of the product after seeing the show, what conclusion can be

reached at the 1% level of significance?

18. In an attitude test, 55 out of 120 persons of Community 1 and 115 persons out of 400 of

Community 2 answered “Yes” to a certain question. Do these two communities differ

fundamentally in their attitudes on this question assuming a 5% level of significance?

20. An advertising company wants to determine if the cartoon series, Voltes V, appeals to

male viewers more than female viewers. Based on random telephone interviews, it was

found that 23 out of 48 females and 41 out of 90 females watch the series regularly. What

should the advertising company conclude at the 5% level of significance?

How do you create your multiple regression formula from your data? I ran my Regression in excel and I have my data, I just don't know how to create the formula.

1. Assume the branch manager is not satisfied with the widths of the obtained confidence intervals, and she requests estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of No Gulf View condominiums with a margin of error of $15,000. Using 95% confidence, how should the sample sizes be?

   Gulf View Condominiums		No Gulf View Condominiums
   List Price	Sale Price	List Price	Sale Price
   495.0	475.0	227.0	227.0
   379.0	350.0	158.0	145.5
   529.0	519.0	196.5	189.0
   552.5	534.5	249.0	240.0
   334.9	334.9	289.0	277.5
   550.0	505.0	225.0	224.0
   169.9	165.0	289.0	269.0
   210.0	210.0	189.9	186.5
   975.0	945.0	159.9	154.9
   314.0	314.0	245.0	240.0
   315.0	305.0	209.8	202.0
   885.0	800.0	220.0	205.0
   975.0	975.0	236.0	222.0
   469.0	445.0	159.9	156.5
   329.0	305.0	170.0	170.0
   365.0	330.0	332.0	302.5
   332.0	312.0	197.5	189.0
   520.0	495.0	257.0	237.0
   425.0	405.0
   675.0	669.0
   409.0	400.0
   649.0	649.0
   319.0	305.0
   425.0	410.0
   359.0	340.0
   469.0	449.0
   895.0	875.0
   439.0	430.0
   435.0	400.0
   235.0	227.0
   638.0	618.0
   629.0	600.0
   329.0	309.0
   595.0	555.0
   339.0	315.0
   215.0	200.0
   395.0	375.0
   449.0	425.0
   499.0	465.0
   439.0	428.5

You may need to use the appropriate appendix table or technology to answer this question. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 32 years of rainfall for California and a sample of 48 years of rainfall for New York has been taken.

b.What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)

c.What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)

d.In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?

Define each of them and show the process of solving them with Excel.

What is critical value/standardized test statistic z/standardized test statistic t/P-value?

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.

If p is any positive number between 0 and 1, then p4 + C(4,3) p3(1–p) + C(4,2) p2(1–p)2 + C(4,1) p (1–p)3 + (1–p)4 = 1. Explain why without performing any calculation.

Please explain the concept behind this to me, and not just the chain of calculations or mathematical proofs.

Six hundred and five survivors of a heart attack, were randomly assigned to follow either (1) a diet close to the "prudent diet step 1" of the American Heart Association or (2) a Mediterranean-type diet consisting of more bread and cereals, more fresh fruit and vegetables, more grains, more fish, fewer delicatessen food, less meat. Over four years, researchers collected information on number of deaths from cardiovascular causes e.g., heart attack and strokes. Of the 303 survivors who followed the AHA diet 24 died of cardiovascular disease. Of the 302 survivors who followed the Mediterranean diet, 14 died of cardiovascular disease. Is there a significant difference in the proportion of patients who die of cardiovascular disease across the two diet plans? Run the test at a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUSTshow your work to receive full credit. Partial credit is available.

As you read about regression this week, try to think of pairs of variables whose values might be associated, or as we say in statistics have a correlation. For example, height and weight have a positive correlation because in general we expect taller people to weigh more than shorter people. This does not mean every taller person weighs more than every shorter person, but that's the tendency. Can you think of another pair of variable that have a positive correlation? How about a pair of variables that have a negative correlation? Try to think of pairs of variables from your field of study! For each variable, consider the following: give a brief description of each variable, how is it measured, what are its possible values, Why do you think the correlation between your two variables is positive or negative?

The following frequency distribution shows the price per share for a sample of 30 companies listed on the New York Stock Exchange.

Compute the sample mean price per share and the sample standard deviation of the price per share for the New York Stock Exchange companies (to 2 decimals). Assume there are no price per shares between 29 and 30, 39 and 40, etc.

Q 4
A computer program translates texts between different languages. Experience shows that the probability of a word being incorrectly translated is 0.002.
We enter a text with 5000 words.
What is the probability that no word is translated incorrectly? (Tips, Po)
What is the probability that at most 2 words will be translated incorrectly?
What is the probability that 3 or more words are translated incorrectly?

The better-selling candies are often high in calories. Assume that the following data show the calorie content from samples of M&M's, Kit Kat, and Milky Way candies.

Test for significant differences among the calorie content of these three candies.

A) State the null and alternative hypotheses.

H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM ≠ Median_KK ≠ Median_MW

H₀: All populations of calories are identical.
H_a: Not all populations of calories are identical.    

H₀: Not all populations of calories are identical.
H_a: All populations of calories are identical.

H₀: Median_MM = Median_KK = Median_MW
H_a: Median_MM > Median_KK > Median_MW

H₀: Median_MM ≠ Median_KK ≠ Median_MW
H_a: Median_MM = Median_KK = Median_MW

B) Find the value of the test statistic. (Round your answer to two decimal places.)

C) Find the p-value. (Round your answer to three decimal places.)

D) At a 0.05 level of significance, what is your conclusion?

Reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.    

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among the calorie content of these three candies.