A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.05 years, with sample standard deviation s = 0.88 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 1.75 yr; H₁: μ < 1.75 yr

H₀: μ < 1.75 yr; H₁: μ = 1.75 yr    

H₀: μ > 1.75 yr; H₁: μ = 1.75 yr

H₀: μ = 1.75 yr; H₁: μ ≠ 1.75 yr

H₀: μ = 1.75 yr; H₁: μ > 1.75 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is known.

The Student's t, since the sample size is large and σ is known.    

The Student's t, since the sample size is large and σ is unknown.

The standard normal, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Find the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.

There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.  

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 49% of all such batches contain no defective components, 33% contain one defective component, and 18% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.

no defective components=?

one defective component=?

two defective components=?

(b) One of the two tested components is defective. [Hint: Draw a tree diagram with three first-generation branches for the three different types of batches.]

no defective components=?

one defective component=?

two defective components=?

A company operates a solar installation in the desert in Western Australia. It is reviewing its operating practices with a view to making them more efficient. The solar installation generates electric power from sunlight and incurs operating costs for cleaning the solar modules (sometimes called solar panels) and replacing solar modules that have failed.

a) The annual revenue from the electric power is variable due to variable cloudiness and solar module failure and has a mean of $2.78m and a standard deviation of $0.32m. The annual operating costs have a mean of $0.51m and a standard deviation of $0.12m. Expected revenue varies systematically from one month to another, being higher in the summer when there is more sunshine. Monthly operating costs follow the same probability model regardless of the month (same mean and standard deviation apply to all months). Calculate, if possible, the mean and standard deviation of (i) monthly operating costs (ii) monthly profits. If a calculation is not possible, give the reason.

Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are as

follows for the past 12 weeks:

WEEK ACTUAL PASSENGER MILES (1,000S)

1            17

2            21

3            19

4            23

5            18

6            16

7            20

8            18

9            22

10         20

11         15

12         22

Assuming an initial forecast for week 1 of 17,000 miles, use exponential smoothing to

compute miles for weeks 2 through 12. Use α = 0.2.

What is the MAD for this model?

Compute the RSFE and tracking signals. Are they within acceptable limits?

PLEASE ANSWER THE RSFE question Thank you

A school administrator is interested in a schools performance in math.  He administers a math test to a sample of 30 students and obtains a mean of 84.25.  The standard deviation of this sample was 8.4. (T Test)

26. Construct a 95% confidence interval for this data.

27. How would you interpret this confidence interval?

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 9. The hypotheses H₀: μ = 75 and H_a: μ < 75 are to be tested using a random sample of n = 25 observations.

(a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.)
standard deviations

(b) If x = 72.3, what is the conclusion using α = 0.002?
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75.Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75.    Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75.Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75.

(c) For the test procedure with α = 0.002, what is β(70)? (Round your answer to four decimal places.)
β(70) =

(d) If the test procedure with α = 0.002 is used, what n is necessary to ensure that β(70) = 0.01? (Round your answer up to the next whole number.)
n =  specimens

(e) If a level 0.01 test is used with n = 100, what is the probability of a type I error when μ = 76? (Round your answer to four decimal places.)

2. (Binomial model) Consider a roulette wheel with 38 slots, of which 18 are red, 18 are black, and 2 are green (0 and 00). You spin the wheel 6 times.

(a) What is the probability that 2 of those times the ball ends up in a green slot? (

b) What is the probability that 4 of those times the ball ends up in a red slot?

3. (Normal approximation to binomial model) Take the roulette wheel from question 2. Assume that the wheel is spun 100 times, and you are interested in whether the ball ends up in a red slot.

(a) Verify that you can use the normal model here.

(b) Find the probability that the ball ends up in a red slot at least 60 times.

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week.

−0.43	−0.22	−0.42	−0.37	+0.27	−0.23	+0.32	+0.54	−0.19
−0.29	−0.34	−0.55	−0.44	−0.56	−0.05	−0.19	−0.24	+0.08

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
4. Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.01 significance level.
5. Estimate the p-value.

Bob is an amoeba that behaves as follows: at the end of any given minute, Bob either splits into two identical and independent copies of himself, stays the same without splitting, or dies; all three of these happen with equal probability. All subsequent Bobs behave identically and independently to the original Bob. If there is only 1 Bob at the start, find the expected number of Bobs after 2 minutes

This was the only information given in the question

In 2012, the Detroit Tigers and the San Francisco Giants met in baseball's World Series.  That year, the Tigers had a won-lost record of 88-74 and the Giants had a won-lost record of 94-68.   The question is whether the Giants were in fact the superior team based on their won-lost record.  So, test the claim that the 'true' proportion of their games won by the Giants was in fact higher than it was for the Tigers in 2012. Assume the only alternate hypothesis of interest is where the Giants are the superior team.   

The p-value of the hypothesis test is: ?????



Which of the following are correct conclusions?

At a 10% significance level, it would appear that the Giants were in fact the superior team.

At a 1% significance level, it would appear that the Giants were in fact the superior team.

At a 5% significance level, it would appear that the Giants were in fact the superior team.

At a 15% significance level, it would appear that the Giants were in fact the superior team.

It would seem that this 6-win difference over the course of the season is not statistically significant.

eBook Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

City	Miles of Track	Ridership (1000s)
Cleveland	17	17
Denver	19	37
Portland	40	83
Sacramento	23	33
San Diego	49	77
San Jose	33	32
St. Louis	36	44 a) Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track. Compute b0 and b1 (to 2 decimals). Complete the estimated regression equation (to 2 decimals). b) Compute the following (to 1 decimal): SSE SST SSR MSE c) What is the coefficient of determination (to 3 decimals)? Note: report r2 between 0 and 1. Does the estimated regression equation provide a good fit? d) Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal). e) Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal). Do you think that the prediction interval you developed would be of value to Charlotte planners in anticipating the number of weekday riders for their new light-rail system?

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first twelve times he filled up the tank, he found the mean was 22.9 miles per gallon (mpg) with a sample standard deviation of 1.2 mpg.

1. Compute the 98% confidence interval for his mpg. (Use t Distribution Table.) (Round your answers to 3 decimal places.)

2. How many times should he fill his gas tank to obtain a margin of error below 0.15 mpg? (Use z Distribution Table.) (Round your answer to the next whole number.)

A study is performed in a large southern town to determine whether the average amount spent on fod per four person family in the town is significantly different from the national average. Assume the national average amount spent on food for a four- person family is $150.

A what is the null and alternative hypothesis?

b. Is the sample evidence significant? significance level?

Family	Weekly food expense
1	$198.23
2	$143.53
3	$207.48
4	$134.55
5	$182.01
6	$189.84
7	$170.36
8	$163.72
9	$155.73
10	$203.73
11	$191.19
12	$172.66
13	$154.25
14	$179.03
15	$130.29
16	$170.73
17	$194.50
18	$171.14
19	$175.19
20	$177.25
21	$166.62
22	$135.54
23	$141.18
24	$158.48
25	$159.78
26	$157.42
27	$98.40
28	$181.63
29	$128.45
30	$190.84
31	$154.04
32	$190.22
33	$161.48
34	$113.42
35	$148.83
36	$197.68
37	$135.49
38	$146.72
39	$176.62
40	$154.60
41	$178.39
42	$186.32
43	$157.94
44	$116.35
45	$136.81
46	$195.58
47	$129.44
48	$146.84
49	$165.63
50	$158.97
51	$210.00
52	$175.46
53	$159.69
54	$154.56
55	$152.95
56	$177.30
57	$129.23
58	$127.40
59	$167.48
60	$183.83
61	$157.39
62	$163.24
63	$165.01
64	$137.43
65	$177.37
66	$142.68
67	$150.04
68	$161.44
69	$166.13
70	$190.96
71	$187.19
72	$116.63
73	$159.73
74	$159.64
75	$142.44
76	$153.03
77	$143.12
78	$156.35
79	$182.70
80	$129.03
81	$119.06
82	$137.99
83	$144.20
84	$183.51
85	$169.67
86	$134.66
87	$202.94
88	$143.43
89	$170.52
90	$139.53
91	$159.31
92	$134.77
93	$165.48
94	$127.20
95	$168.16
96	$125.39
97	$167.96
98	$178.64
99	$134.38
100	$111.87

A.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.9 years, and standard deviation of 1 years. If you randomly purchase one item, what is the probability it will last longer than 9 years?

B.) A particular fruit's weights are normally distributed, with a mean of 784 grams and a standard deviation of 24 grams. If you pick one fruit at random, what is the probability that it will weigh between 845 grams and 859 grams.

C.) A particular fruit's weights are normally distributed, with a mean of 615 grams and a standard deviation of 11 grams. The heaviest 19% of fruits weigh more than how many grams?
Give your answer to the nearest gram.

D.) A distribution of values is normal with a mean of 228.7 and a standard deviation of 33.7. Find P₈₅, which is the score separating the bottom 85% from the top 15%.
P₈₅ =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

E.) The combined SAT scores for the students at a local high school are normally distributed with a mean of 1470 and a standard deviation of 303. The local college includes a minimum score of 2137 in its admission requirements.
What percentage of students from this school earn scores that satisfy the admission requirement?
P(X > 2137) = %
Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

7.16 How do you position yourself when you are going to sleep? A website tells us that 41% of use start in the fetal position, another 28% start on our side with legs straight, 13% start on their back, and 7% on their stomach. The remaining 11% have no standard starting sleep position. If a random sample of 1000 people produces the frequencies in the table below, should you doubt the proportions given in the article in the website? Show all the details of the test, and use a 5% significance level.

Sleep Position	Frequency
Fetal	391
Side, legs straight	257
Back	156
Stomach	89
None	107
Total	1000