2.The weights of four randomly and independently selected bags of potatoes labeled 20 pounds were found to be 21, 22​, ,20.4, and 21.2

Assume Normality.

a. Using a​ two-sided alternative​ hypothesis, should you be able to reject the hypothesis that the population mean is 20

pounds using a significance level of 0.05

Why or why​ not? The confidence interval is reported​ here: I am

95​%confident the population mean is between 20.1 and 22.2pounds.

b. Test the hypothesis that the population mean is not 20

Use a significance level of 0.05

c. Choose one of the following​ conclusions:

i. We cannot reject a population mean of 20 pounds.

ii. We can reject a population mean of 20 pounds.

iii. The population mean is 21.15 pounds.

A pizza restaurant monitors the size (measured by the diameter) of the 10-inch pizzas that it prepares. Pizza crusts are made from doughsthat are prepared and prepackaged in boxes of 15 by a supplier. Doughsare thawed and pressed in a pressing machine. The toppings are added, and the pizzas are baked. The wetness of the doughsvaries from box to box, and if the dough is too wet or greasy, it is difficult to press, resulting in a crust that is too small. The first shift of workers begins work at 4 P.M., and a new shift takes over at 9 P.M. and works until closing. The pressing machine is readjusted at the beginning of each shift. The restaurant takes five consecutive pizzas prepared at the beginning of each hour from opening to closing on a particular day. The diameter of each baked pizza in the subgroups is measured, and the pizza crust diameters obtained are given in Table.

Use the pizza crust diameter data to do the following:

a. Show that X bar =10.028 and R bar = 0.84.

b. Find the center lines and control limits for the X bar and Rcharts for the pizza crust data.

c. Set up the X bar and Rcharts for the pizza crust data.

d. Is the R chart for the pizza crust data in statistical control? Explain.

e. Is the X bar chart for the pizza crust data in statistical control? If not, use the X bar chart and the information given with the data to try to identify any assignable causes that might exist.

f. Suppose that, based on the X bar chart, the manager of the restaurant decides that the employees do not know how to properly adjust the dough pressing machine. Because of this, the manager thoroughly trains the employees in the use of this equipment. Because an assignable cause (incorrect adjustment of the pressing machine) has been found and eliminated, we can remove the subgroups affected by this unusual process variation from the data set. We therefore drop subgroups 1 and 6 from the data. Use the remaining eight subgroups to show that we obtain revised center lines of X bar = 10.2225 and R bar = 0.825.

g. Use the revised values of and to compute revised and R chart control limits for the pizza crust diameter data. Set up X bar and R charts using these revised limits. Be sure to omit subgroup means and ranges for subgroups 1 and 6 when setting up these charts.

h. Has removing the assignable cause brought the process into statistical control? Explain.

Dana uses the following parameters to determine that she needs a sample size of 140 participants for her study that will compare the means of two independent groups (t-test) using a one-tailed hypothesis:

            Effect size (d) = .5

            alpha = .05

            Power (1 - beta) = .90

Using the above information, answer each of the following questions.

a. If Dana keeps alpha and sample size the same, but desires an effect size of .80, what will happen to power? Will it increase or decrease? Explain.

b. If Dana keeps the desired effect size and sample size the same, but reduces alpha to .025, what will happen to power? Will it increase or decrease? Explain.

c. If Dana keeps power and sample size the same, but increases the desired effect size to .8, what will happen to alpha? Will it increase or decrease? Explain.

d. Dana decides she wants to increase the desired effect size to 2.0 and increase the power to .99, but keeps alpha the same. She does so to increase the likelihood that an effect will be found, and to make sure her results demonstrate a large enough effect. Also, when she conducts her a priori power analysis to determine her sample size, she is excited to see that she needs far fewer participants in her sample with those parameters (target n = 18). What, if any, are the problems with Dana’s strategy?

Answer the questions as indicated for scenarios 1-5. Note: You do not need to perform any of the procedures indicated.

Scenario 3: A guidance counselor identifies a random sample of 40 high school female students and gives each of these students a vocabulary test. For the female group, the average vocabulary score was 69 with a standard deviation of 5.3. Next, the guidance counselor takes a random sample of 48 male high school students. The male students also complete the vocabulary test. This group had an average vocabulary score of 64 with a standard deviation of 5.6. What is a 90% confidence interval estimate for difference in average vocabulary test score between female and male students at this school?

A. Indicate whether the inference procedure needed is a confidence interval or a significance test.

B. Indicate whether the procedure involves one or two samples.

C. Name the inference method needed to answer the question posed.

D. Verify whether or not the conditions have been met for this inference procedure. Specifically, you need to list each condition and then explain how the condition was or was not met.

E. Determine if it is appropriate to perform the significance test or confidence interval (yes/no).

Find the mean, mod, median, and standard deviation of the following data. And Based on these results, check whether the value of 10 is usual? 5, 6, 7, 8, 9,8,7,8 _________________________________________________________________________ Pre-Employment Drug Screening Results are shown in the following Table: Positive Test Result Negative Test Result Subject Uses Drugs 8 (True Positive) 2 (False Negative) Subject is not a Drug User 10 (False Positive) 180 (True Negative) If 1 of the 200 test subjects is randomly selected, find the probability that the subject had a positive test result, given that the subject actually uses drugs. That is, find (positive test result subject uses drugs). If 1 of the 200 test subjects is randomly selected, find the probability that the subject actually uses drugs, given that he or she had a positive test result. That is, find ( subject uses drugs positive test result ). _______________________________________________________________________ This is observation from previous years about the impact of students working while they are enrolled in classes, due to students too much work, they are spending less time on their classes. First, the observer need to find out, on average, how many hours a week students are working. They know from previous studies that the standard deviation of this variable is about 5 hours. A survey of 200 students provides a sample mean of 7.10 hours worked. What is a 95% confidence interval based on this sample?

A survey was conducted among 20 adults. The following shows the age of the respondents.

44 47 47 47 47 52 53 53 54 54

55 56 57 58 58 64 66 66 69 83

(1) Please calculate the mean, median, 1st quartile (i.e. 25th percentile), 3rd quartile (i.e. 75th percentile), and IQR for their age. (2 points for each question, 10 points in total)

(2) For the above 20 adults, are there outliers (i.e. are there people with extreme age)? Please show your calculations for identifying the outliers. (2 points)

2.Thirty GPAs from a randomly selected sample of statistics students at a college are linked below. Assume that the population distribution is approximately Normal. The technician in charge of records claimed that the population mean GPA for the whole college is 2.81. a. What is the sample​ mean? Is it higher or lower than the population mean of 2.81​? b. The chair of the mathematics department claims that statistics students typically have higher GPAs than the typical college student. Use the​ four-step procedure and the data provided to test this claim. Use a significance level of 0.05.

2.86,3.37,3.17,2.51,3.49, 2.75, 3.04, 3.59,2.65,3.97,2.89,2.66,3.52,3.06, 2.79,3.45,2.47,3.14,3.43,3.13,3.18,3.08,3.09,2.96,3.49, 3.43,2.73,3.14, 3.11,3.03

In Country​ A, the population mean height for​ 3-year-old boys is 37 inches. Suppose a random sample of 15​ 3-year-old boys from Country B showed a sample mean of 36.5 inches with a standard deviation of 4 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Complete parts a through c below. a. Determine whether the population mean for Country B boys is significantly different from the Country A mean. Use a significance level of 0.05. Find test statistic and p-value b. Now suppose the sample consists of 30 boys instead of 15 and repeat the test. Find the test statistic and p- value

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.