An article reports measurements of the total power, on the log scale, of the heart rate variability, in the frequency range 0.003 to 0.4 Hz, for a group of 40 patients aged 25–49 years and for a group of 43 patients aged 50–75 years. The mean for the patients aged 25–49 years was 4 with a standard deviation of 0.23, and the mean for the patients aged 50–75 years was 3.4 with a standard deviation of 0.28. Let μX represent the population mean for the patients aged 25-49 years and let μY represent the population mean for the patients aged 50-75 years. Find a 95% confidence interval for the difference μX−μY. Round the answers to three decimal places.

The 95% confidence interval is ( , ).

1A) The proportions of defective parts produced by two machines were compared, and the following data were collected. Determine a 90% confidence interval for p₁ - p₂. (Give your answers correct to three decimal places.)

Lower Limit -

Upper Limit -

1B) Find the value of t for the difference between two means based on an assumption of normality and this information about two samples. (Use sample 1 - sample 2. Give your answer correct to two decimal places.)

How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity: 58 52 68 86 72 66 97 89 84 91 91 92 66 68 87 86 73 61 70 75 72 73 85 84 90 57 77 76 84 93 58 47 (a) Make a stem-and-leaf display for these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Longevity of Cowboys 4 5 6 7 8 9 7 2788 16688 02233567 44456679 011237 (b) Consider the following quote from Baron von Richthofen in his Cattle Raising on the Plains of North America: "Cowboys are to be found among the sons of the best families. The truth is probably that most were not a drunken, gambling lot, quick to draw and fire their pistols." Does the data distribution of longevity lend credence to this quote? No, these cowboys did not live long lives, as evidenced by the high frequency of leaves for stems 4 and 5 (i.e., 40- and 50-year-olds). Sort of, these cowboys lived somewhat long lives, as evidenced by the high frequency of leaves for stems 5 and 6 (i.e., 50- and 60-year-olds). Yes, these cowboys certainly lived long lives, as evidenced by the high frequency of leaves for stems 7, 8, and 9 (i.e., 70-, 80-, and 90-year-olds). 6.–/2.85 points BBUnderStat12 2.1.017. Ask Your Teacher My Notes Question Part Points Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy (Reference: D.P. Byar, Journal of Urology, Vol. 10, pp. 556-561). 19 18 17 1 21 22 54 46 25 49 50 1 59 39 43 39 5 9 38 18 14 45 54 59 46 50 29 12 19 36 38 40 43 41 10 50 41 25 19 39 27 20 For this problem, use five classes. (a) Find the class width. 12 (b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 2 decimal places.) Class Limits Class Boundaries Midpoint Frequency Relative Frequency Cumulative Frequency 1 − 12 13 − 24 25 − 36 37 − 48 49 − 60 0.5 − 12.5 12.5 − 24.5 24.5 − 36.5 36.5 − 48.5 48.5 − 60.5 6.5 18.5 30.5 42.5 54.5 6 10 5 13 8 0.14 0.24 0.12 0.31 0.19 6 10 21 34 42 (c) Draw a histogram. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Draw a relative-frequency histogram. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (e) Categorize the basic distribution shape. uniform mound-shaped symmetrical bimodal skewed left skewed right

Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.8%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1

The sample mean is x bar = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 5.0%. Do these data indicate that the dividend yield of all bank stocks is higher than 5.0%? Use α = 0.01.

Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.)

Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.)

A study of reading comprehension in children compared three methods of instruction. The three methods of instruction are called Basal, DRTA, and Strategies. As is common in such studies, several pretest variables were measured before any instruction was given. One purpose of the pretest was to see if the three groups of children were similar in their comprehension skills. The READING data set described in the Data Appendix gives two pretest measures that were used in this study. Use one-way ANOVA to analyze these data and write a summary of your results.

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

subject group   pre1    pre2    post1   post2   post3
1       B       4       3       5       4       41
2       B       6       5       9       5       41
3       B       9       4       5       3       43
4       B       12      6       8       5       46
5       B       16      5       10      9       46
6       B       15      13      9       8       45
7       B       14      8       12      5       45
8       B       12      7       5       5       32
9       B       12      3       8       7       33
10      B       8       8       7       7       39
11      B       13      7       12      4       42
12      B       9       2       4       4       45
13      B       12      5       4       6       39
14      B       12      2       8       8       44
15      B       12      2       6       4       36
16      B       10      10      9       10      49
17      B       8       5       3       3       40
18      B       12      5       5       5       35
19      B       11      3       4       5       36
20      B       8       4       2       3       40
21      B       7       3       5       4       54
22      B       9       6       7       8       32
23      D       7       2       7       6       31
24      D       7       6       5       6       40
25      D       12      4       13      3       48
26      D       10      1       5       7       30
27      D       16      8       14      7       42
28      D       15      7       14      6       48
29      D       9       6       10      9       49
30      D       8       7       13      5       53
31      D       13      7       12      7       48
32      D       12      8       11      6       43
33      D       7       6       8       5       55
34      D       6       2       7       0       55
35      D       8       4       10      6       57
36      D       9       6       8       6       53
37      D       9       4       8       7       37
38      D       8       4       10      11      50
39      D       9       5       12      6       54
40      D       13      6       10      6       41
41      D       10      2       11      6       49
42      D       8       6       7       8       47
43      D       8       5       8       8       49
44      D       10      6       12      6       49
45      S       11      7       11      12      53
46      S       7       6       4       8       47
47      S       4       6       4       10      41
48      S       7       2       4       4       49
49      S       7       6       3       9       43
50      S       6       5       8       5       45
51      S       11      5       12      8       50
52      S       14      6       14      12      48
53      S       13      6       12      11      49
54      S       9       5       7       11      42
55      S       12      3       5       10      38
56      S       13      9       9       9       42
57      S       4       6       1       10      34
58      S       13      8       13      1       48
59      S       6       4       7       9       51
60      S       12      3       5       13      33
61      S       6       6       7       9       44
62      S       11      4       11      7       48
63      S       14      4       15      7       49
64      S       8       2       9       5       33
65      S       5       3       6       8       45
66      S       8       3       4       6       42

An investment analyst prepares the following distribution of the prices of two equity stocks, A and B, she expects to see at the end of the coming financial year in each of five states. The probability that each state might occur has also been estimated and is noted below. The current prices in the market are £45 and £38 per share for A and B respectively.

1. For both stocks A and B, calculate the expected return, the variance of the returns and the inter-quartile range of the returns.

2. Calculate the covariance between the returns of A and B.

3. Calculate the correlation between the returns of A and B, using the correlation function in Excel, as well as, directly using formulae. Explain the difference in the two correlation values.

4. For both stocks A and B, calculate the negative semi-variance of the return at the end of the year. Why might investors take account of the negative semi-variance of the returns as a measure of risk?

Q6 The weight of adults in USA is normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds. What is the probability that a single adult will weigh more than 190 pounds?

Q7 Along the lines of Q6 above, what is the probability that 25 randomly selected adults will have a MEAN more than 190 pounds?

Q8 Along the lines of Q6 above, an elevator has a sign that says that the maximum allowable weight is 4750 pounds. If 25 randomly selected people cram into the elevator, what is the probability that it will be over the maximum allowable weight?

Q9 The human gestation period (pregnancy period) is normally distributed with a mean of 268 days and a standard deviation of 15 days. If 25 women are randomly selected, find the probability that the sample will have a mean of less than 260 days.

Q10 Along the lines of Q9 above, a random selection of 25 woman (volunteers) are put on a special diet and the sample mean is less than 260 days. Does it appear that the diet has an effect of gestation period? What could make you more “certain”?

Suppose µ is the mean of a normally distributed population for which the standard deviation is known to be 3.5. The hypotheses H0 : µ = 10 Ha : µ 6= 10 are to be tested using a random sample of size 25 from the population. The power of an 0.05 level test when µ = 12 is closest to

3. A homeowner wants to purchase multiple electric pumps and operate them in parallel to ensure that she can handle any basement flooding that occurs. A single electric pump is enough to handle any flooding, but the pumps are not very reliable. She wants to be %99.99 sure that there will be a working pump during a flood.

   1. (a) If she only wants to buy 3 identical electric pumps, what is the required minimum reliability of each pump?

   2. (b) Now suppose the manufacturer specifies each electric pump has a 0.75 reliability. How many would need to be purchased?

   3. (c) After some searching, another more reliable gas-powered pump with the same output capacity as the electric pump was found. These gas-powered pumps have a reliability of 0.85 but cost $1000 dollars each. The electric pumps cost $600. If she is going to buy only one type of pump, what is the cheapest option to meet her reliability goal? What if she is willing to buy both kinds of pumps?

A study of 420 comma 059 cell phone users found that 130 of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be 0.0438​% for those not using cell phones. Complete parts​ (a) and​ (b). a. Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

2. Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals 934 and x equals 524 who said​ "yes." Use a 95 % confidence level. ​b) Identify the value of the margin of error E.

consider a standard deck of playing cards... 52 cards, 4 suits of 13 cards each, 3 cards of each suit are face cards, 2 suits are black (clubs and spades) and 2 are red (hearts and diamond)

a) Let event A be drawing a random card that is a diamond. What is a trial for this scenario? What is the sample space? Is A a simple event? What is P(A)? What is A¯, the complement of A? What is P(A¯)?

b) Let event A be drawing a random card that is a diamond. Let event B be drawing a random card that is a face card. Are events A and B disjoint? What is P(A or B)?

c) Consider drawing three cards. Let event A be the first card is a heart. Let event B be the second card is a club. Let event C be the third card is black. Are events A, B and C independent? What is P(A and B and C)?

The number of earthquakes that occur per week in California follows a Poisson distribution with a
mean of 1.5.
(a) What is the probability that an earthquake occurs within the first week? Show by hand and
provide the appropriate R code.
(b) What is the expected amount of time until an earthquake occurs?
(c) What is the standard deviation of the amount of time until two earthquakes occur?
(d) What is the probability that it takes more than a month to observe 4 earthquakes? Show by hand
(you may simply leave it as an integral) and provide the appropriate R code.
(e) What is the median amount of time it takes for 5 earthquakes to occur? Show by hand (you may
simply leave it as an integral, but be sure to explain how to find the median) and provide the
appropriate R code.

Data represent the effects of food and/or water deprivation on behavior. Treatments 1 and 2 represent control conditions; animal received ad lib food and water (1) or else food and water twice per day (2). In treatment 3 animals were food deprived, in treatment 4 they were water deprived, and in treatment 5 they were deprived of both food and water. The dependent variable is the number of trials to reach a predetermined criterion. Assume we compared the combined control groups (treatments 1 and 2) with the combined experimental groups, the control groups with each other, the singly deprived treatments with the doubly deprived treatment, and the singly deprived treatments with each other

1. Fill out the table below based on the comparisons (linear contrasts)

2. Compute:

Sum ajbj

Sum ajcj

Sum ajdj

Sum bjcj

Sum bjdj

Sum cjdj

Are the four contrasts orthogonal? Explain.

3. Use the results of your computations for part a) to complete the following table.

4. Interpret the results for Contrast 1.
5. Taking into account all four contrasts, what do the results tell us about the effect of food/ water deprivation on the learning task?

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 309 people over the age of​ 55, 76 dream in black and​ white, and among 288 people under the age of​ 25, 17 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts​ (a) through​ (c) below.

Use Affordability, Quality, and Style as the only Values for your decision in finding the best computer for you among 3 computers you have identified as your choices. Apply the Multifactor Evaluation Process by

(i) assigning normalised weights to the Values, (w1=.1 w2=.5 w3=.4)

(ii) assigning for each value, ratings of individual computers.

(iii) Computing the total score of each computer to find the best computer; i.e., the computer with the highest total score.

(iv) Normalizing the ratings and total scores.

You must show systematically all numerical results to receive full credits.