Now let's use Bayes' theorem and the binomial distribution to address a Bayesian inference question. You toss a bent coin N times, obtaining a sequence of heads and tails. The coin has an unknown bias f of coming up heads. (a) If NH heads have occurred in N tosses, what is the probability distribution of f? Assume a uniform prior P(f) = 1 and make use of the following result: integral 0 to 1 f^a (1 - f)^b df = a!b! / (a + b + 1)! (b) Sketch (or plot) the shape of the probability distribution of f for N = 5 and NH = 2. (c) Now derive a formula for the most probable value of f (the most probable value of f, denoted f ', is the value of f that maximizes the probability distribution in (a)). What is f ' for N = 5 and NH = 2. Hint: maximize log P(f | NH, N) rather than P(f | NH, N).

A manager of a pizza restaurant has changed the​ restaurant's delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 30 minutes. A sample of 49 orders using the new delivery process yields a sample mean of 27.7 minutes and a sample standard deviation of 6 minutes.

a.) Using the critical value​ approach, at the 0.05 level of​ significance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes? State the null and alternative hypotheses for this test.

        What is the test statistic for this​ test? (Type an integer or a decimal. Round to two decimal places as​ needed.)

        What​ is(are) the critical​ value(s) for this​ test? ​(Type an integer or a decimal. Round to two decimal places as needed. Use commas to separate your answers as​ needed.)

       What is the conclusion for this​ test? Since the test statistic is ___________than the critical​ value, __________the null hypothesis and conclude that there is ___________evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes.

b.) . Using the​ p-value approach, at the 0.05 level of​ significance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes?

        What is the​ p-value for this​ test? (Type an integer or a decimal. Round to three decimal places as​ needed.)

        What is the conclusion for this​ test?

        Since the​ p-value is __________ than α _________the null hypothesis and conclude that there is ___________evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes.

c.) Interpret the meaning of the​ p-value in this problem.

d.) d. Compare your conclusions in​ (a) and​ (b).

. Use StatsDisk

Find the Mean, Median, Variance and Standard Deviation of the data below?

Females

1-6

2-1

3-1

4-4

5-6

6-8

7-2

8-2

9-4

10-5

11-7

12-10

13-6

14-3

15-2

16-1

17-Something

...........

18-1

19-2

20-3

21-5

22-7

23-8

24-2

25-3

26-2

27-2

28-4

29-3

30-4

31-6

32-1

33-1

34-6

35-4

36-4

37-3

38-1

39-1

40-5

41-8

42-1

43-7

44-9

45-2

46-9

47-7

48-8

49-4

............

50-2

51-1

52-Sometimes

53-1

54-2

55-3

56-3

57-3

58-2

59-2

60-4

61-5

62-5

63-2

64-1

65-7

66-2

67-1

68-8

69-8

70-8

71-3

72-4

73-5

74-9

75-9

76-10

77-1

78-2

79-3

................

80-5

81-5

82-3

83-1

84-2

85-6

86-7

87-7

88-1

89-3

90-2

91-4

92-4

93-6

94-6

95-7

96-1

97-3

98-8

99-7

100-5

For a t-distribution with 15 degrees of freedom, 90% of the distribution is within how many standard deviations of the mean?

Select one: a. 1.235 b. 1.576 c. 1.753 d. 1.960

The time required for a student to complete an Economics 110 exam is normally distributed with a mean of 54 minutes and a standard deviation of 16 minutes.

5. ______ What percentage of students will complete the exam in less than 75 minutes (before end of class period)? (A) .4049 (B) .9951 (C) .8051 (D) .9049

6. ______ At what point in time (i.e., how long after the exam starts) will one-third of all students have finished taking the exam? (A) 25 minutes (B) 60.9 minutes (C) 47.1 minutes (D) 38.5 minutes

7. ______ In a class of 50 students taking an Economics 110 exam, what is the probability that the average time required to take the exam will be more than 60 minutes? (A) .4960 (B) .0040 (C) .1480 (D) .3520

Duracell released an advanced long lasting AAA battery, which it claims can last on average for at least 200 days with the standard deviation of 16 days in any remote control devices. A random sample of 100 batteries was selected and the results showed that new batteries lasted on average for 198 days. Construct 90% confidence interval for the population mean and interpret it. Also conduct the five-step hypothesis test at α = 0.05 to determine whether the battery manufacturer’s claim is true or not and afterwards, compute the p-value for it.

An appraiser is appraising an office building in Manhattan. Assume that the population of these appraisals is normally distributed. For commercial appraisals, a comparison analysis and a cost analysis is done. A comparison analysis involves finding the sale prices of several comparable properties (within the last six months) and computing an average value. The cost method involves determining the present cost of duplicating the given property. Clearly, if the comparable analysis yields a present market price greater than the cost of duplicating the given property, the price is not a good deal to an investor, and vice versa. Using the comparison analysis method, the appraiser collected sales data on nine comparable buildings, yielding values of $111,520,000, $112,460,000, $111,940,000, $112,601,000, $110,980,000, $111,200,000, $112,750,000, $112,400,000, and $111,680,000. Using the cost approach, the appraisal was $112,525,000. At the 5% level of significance, should the appraiser conclude that the two appraisals are the same or different?

Step 1 of 4: Consider the problem scenario. The mean of the comparable properties is $111,948,000. What are the logical hypotheses? Use a significance level of 5%.

A) H₀: μ  ≤  $112,525,000 H_a: μ > $112,525,000

B) H₀: μ = $112,525,000 H_a: μ ≠ $112,525,000

C) H₀: μ ≠ $112,525,000 H_a: μ = $112,525,000

D) H₀: μ ≥  $112,525,000 H_a: μ <  $112,525,000

Step 2 of 4: What is the classical approach decision rule for the null hypothesis?

A) If | t |  <  1.860, reject the null hypothesis.

B) If t  >  1.860, reject the null hypothesis.

C) If t  <  -1.860, reject the null hypothesis.

D) If | t |  >  1.860, reject the null hypothesis.

Step 3 of 4: Using the classical approach, state the conclusion of the test.

A) It is a certainty that the comparison appraisal is less than the cost appraisal.

B) At the 5% level, fail to reject the null hypothesis; there is not sufficient sample evidence to claim that the comparison appraisal is less than the cost appraisal.

C) At the 5% level, reject the null hypothesis; there is sufficient sample evidence to conclude that the comparison appraisal is less than the comparison appraisal is less than the cost appraisal.

D) At the 5% level, the results are inconclusive.

Step 4 of 4: Using the p-value approach, state the conclusion of the test.

A) Since the p-value of 0.000 is less than the stated significance level of 0.05, the test is inconclusive.

B) Since the p-value of 0.100 is not less than the stated significance level of 0.05, fail to reject the null hypothesis

C) Since the p-value of 0.027 is less than the stated significance level of 0.05, fail to reject the null hypothesis

D) Since the p-value of 0.014 is less than the stated significance level of 0.05, reject the null hypothesis

The given data represent the total compensation for 10 randomly selected CEOs and their​ company's stock performance in 2009. Analysis of this data reveals a correlation coefficient of requals=negative 0.2324−0.2324.

What would be the predicted stock return for a company whose CEO made​ $15 million? What would be the predicted stock return for a company whose CEO made​ $25 million?

What would be the predicted stock return for a company whose CEO made​ $ 15 million?

What would be the predicted stock return for a company whose CEO made​ $ 25 million

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 90 and standard deviation σ = 20. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)

(a) x is more than 60


(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 125 (borderline diabetes starts at 125)

Cavalier Bike co sells their comfortable style bike for $90. Labor, material and overhead are listed:

  Week 1 Week 2 Week 3 Week 4

#Bikes produced      1,117    1,306   1,092      985

Labor ($) 12,691 14,842 10,563     9,576

Material ($)   21,427   24,523     20,442     18,414

Overheads ($) 9,463   10,530   8,686   7,798

What is the multifactor productivity for each week?

Round your answer to the nearest whole number.

A Telecommunications company recently installed a new speech recognition system for its repair calls. In their old system, operators had to press keys on the numeric keypad to answer questions, which led to longer time on service calls. on service calls. The company is conducting a study to examine the impact of the new system on the average duration of service calls. Average duration of service calls was 31.4 minutes prior to the installation of the new system. They analyzed a random sample of 20 service calls and obtained an average duration of service calls of 29.4 minutes. Based on historical data, the standard deviation of duration of service calls is known to be σ =6.2 minutes.

What is the P value of the the hypothesis test to determine if the system has been effective reducing the average duration of service calls ? (Use 4 DECIMALS)

You want to estimate the mean weight of quarters in circulation. A sample of 50 quarters has a mean weight of 5.643 grams and a standard deviation of 0.065 grams. Use a single value to estimate the mean weight of all quarters.​ Also, find the​ 95% confidence interval for the average weight of all quarters. Q- The mean weight of all quarters is approximately ? grams Q- The lower limit of the​ 95% confidence interval is ? Q- The upper limit of the​ 95% confidence interval is? Q- Thus, the​ 95% confidence interval for the average weight of all quarters ranges from ? grams to ? grams.

A genetic experiment with peas resulted in one sample of offspring that consisted of 416 green peas and 156 yellow peas.

a. Construct a 90​% confidence interval to estimate of the percentage of yellow peas.

b. It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

What are differences between in precision analysis for a calibration fit in comparison to a standard scatter analysis?

Describe the theory behind linear regression analysis.

1. Moving Averages.  Use the below actual sales to calculate a three-year average which will be used as the forecast for next periods (chapter 14, text).
2. Exponential Smoothing. Use the same data to forecast sales for the next periods with α=.40 (chapter 14, text).
3. Regression Analysis on Excel. Draw a scatter graph from Insert/Graph/Scatter graph selections in Excel (chapter 15, text).