part 1
An independent measures study was conducted to determine whether a new medication called "Byeblue" was being tested to see if it lowered the level of depression patients experience. There were two samples, one that took ByeBlue every day and one that took a placebo every day. Each group had n = 30. What is the df value for the t-statistic in this study?
a. 60
b. 58
c. 28
d.  There is not enough information

part 2.
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.2-in and a standard deviation of 0.8-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 3.9% or largest 3.9%.

What is the minimum head breadth that will fit the clientele?
min =

What is the maximum head breadth that will fit the clientele?
max =

Do not round your answer.

In how many ways can a five horse race end, allowing for the possibility that

two horses tie?

A phone manufacturer wants to compete in the touch screen phone market. Management understands that the leading product has a less than desirable battery life. They aim to compete with a new touch phone that is guaranteed to have a battery life more than two hours longer than the leading product. A recent sample of 65 units of the leading product provides a mean battery life of 5 hours and 39 minutes with a standard deviation of 92 minutes. A similar analysis of 51 units of the new product results in a mean battery life of 7 hours and 53 minutes and a standard deviation of 83 minutes. It is not reasonable to assume that the population variances of the two products are equal. Use Table 2. Sample 1 is from the population of new phones and Sample 2 is from the population of old phones. All times are converted into minutes. Let new products and leading products represent population 1 and population 2, respectively. a. Set up the hypotheses to test if the new product has a battery life more than two hours longer than the leading product. H0: μ1 − μ2 = 120; HA: μ1 − μ2 ≠ 120 H0: μ1 − μ2 ≥ 120; HA: μ1 − μ2 < 120 H0: μ1 − μ2 ≤ 120; HA: μ1 − μ2 > 120 b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic b-2. Implement the test at the 5% significance level using the critical value approach. Do not reject H0; there is no evidence that the battery life of the new product is more than two hours longer than the leading product. Reject H0; there is no evidence that the battery life of the new product is more than two hours longer than the leading product. Do not reject H0; there is evidence that the battery life of the new product is more than two hours longer than the leading product. Reject H0; there is evidence that the battery life of the new product is more than two hours longer than the leading product.

In a survey, 38% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too high, so he randomly selected 150 pet owners and discovered that 53 of them spoke to their pet on the telephone. Does the vet have a right to be skeptical? use the confidence interval .1 level of significance. a) because np0(1-p0)= blank (=, not equal, greater, or less than) 10, the sample size is (blank- less or greater) 5% of the population size and the sample (blank-) the requirements for testing the hypothesis (blank- are or are not) satisfied. b)what are the null and alternative hypotheses? c)determine the test statistic. d)determine the critical values. e) does the vet have a right to be skeptical?

Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study examined the effect of jumping on the bone density of growing rats. There were three treatments: a control with no jumping, a low-jump condition (the jump height was 30 centimeters), and a high-jump condition (60 centimeters). After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats (expressed in mg/cm3 ) was measured. Here are the data. data126.dat

(a) Make a table giving the sample size, mean, and standard deviation for each group of rats. Consider whether or not it is reasonable to pool the variances. (Round your answers for x, s, and s_(x^^\_) to one decimal place.)

Group n x^^\_ s s_(x^^\_)

Control

Low jump

High jump

(b) Run the analysis of variance. Report the F statistic with its degrees of freedom and P-value. What do you conclude? (Round your test statistic to two decimal places and your P-value to three decimal places.)

F =

P =

Conclusion: There is no? or a? statistically significant difference between the three treatment means at the α = .05 level.

obs     group   g       density
1       Control 1       565
2       Control 1       598
3       Control 1       611
4       Control 1       601
5       Control 1       623
6       Control 1       607
7       Control 1       595
8       Control 1       649
9       Control 1       620
10      Control 1       576
11      Lowjump 2       629
12      Lowjump 2       645
13      Lowjump 2       626
14      Lowjump 2       653
15      Lowjump 2       633
16      Lowjump 2       639
17      Lowjump 2       624
18      Lowjump 2       639
19      Lowjump 2       643
20      Lowjump 2       622
21      Highjump        3       619
22      Highjump        3       614
23      Highjump        3       606
24      Highjump        3       608
25      Highjump        3       615
26      Highjump        3       608
27      Highjump        3       620
28      Highjump        3       619
29      Highjump        3       597
30      Highjump        3       593

Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results. Use a 0.05 significance level and determine if it is reasonable to conclude that the number of absences has decline? Use this information to solve the following questions.

A. What is the null hypothesis statement for this problem?

B. What is the alternative hypothesis statement for this problem?

C. What is alpha for this analysis?

D. What is the most appropriate test for this problem? (choose one of the following)

a. t-Test: Paired Two Sample for Means

b. t-Test: Two-Sampled Assuming Equal Variances

c. t-Test: Two-Sample Assuming Unequal Variances

d. z-Test: Two Sample for Means

E. What is the value of the test statistic for the most appropriate analysis?

F. What is the lower bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

G. What is the upper bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

H. Is it reasonable to conclude that the number of absences has decline? (choose one of the following)

a. Yes

b. No

I. What is the p-value for this analysis? (Hint: Use this value to double check your conclusion)

Show all work with the right formulas

Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, one in the Little River Area and the other in Murrells Inlet. The quality assurance Department wishes to compare the mean waiting times for patients at the two locations. Assume the population standard deviations are not the same. At the 0.05 significance level, is there a difference in the mean waiting time? Samples of the waiting times, reported in minutes, follows: Use the information above to solve the following questions:

A. What is the null hypothesis statement for this problem?

B. What is the alternative hypothesis statement for this problem?

C. What is alpha for this analysis?

D. What is the most appropriate test for this problem? (choose one of the following)

a. t-Test: Paired Two Sample for Means

b. t-Test: Two-Sampled Assuming Equal Variances

c. t-Test: Two-Sample Assuming Unequal Variances

d. z-Test: Two Sample for Means

E. What is the value of the test statistic for the most appropriate analysis?

F. What is the lower bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

G. What is the upper bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

H. It is reasonable to conclude that the mean waiting times are different? (choose one of the following)

a. Yes

b. No

I. What is the p-value for this analysis? (Hint: Use this value to double check your conclusion)

Show all work clearly with the right formulas.

We need to find the confidence interval for the SLEEP variable. To do this, we need to find the mean and standard deviation with the Week 1 spreadsheet. Then we can the Week 5 spreadsheet to find the confidence interval.

First, find the mean and standard deviation by copying the SLEEP variable and pasting it into the Week 1 spreadsheet. Write down the mean and the sample standard deviation as well as the count. Open the Week 5 spreadsheet and type in the values needed in the green cells at the top. The confidence interval is shown in the yellow cells as the lower limit and the upper limit.

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets.
2. Give and interpret the 99% confidence interval for the hours of sleep a student gets
3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs.

In the Week 2 Lab, you found the mean and the standard deviation for the HEIGHT variable for both males and females. Use those values for follow these directions to calculate the numbers again.

(From Week 2 Lab: Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table. Click in the top box and select all the data (including labels) from Height through Gender. Also click on “new worksheet” and then OK. On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values box.   Click on the down arrow next to Height in the Values box and select Value Field Settings. In the pop up box, click Average then OK. Write these down. Then click on the down arrow next to Height in the Values box again and select Value Field Settings. In the pop up box, click on StdDev then OK. Write these values down.)

You will also need the number of males and the number of females in the dataset. You can either use the same pivot table created above by selecting Count in the Value Field Settings, or you can actually count in the dataset.

Then use the Week 5 spreadsheet to calculate the following confidence intervals. The male confidence interval would be one calculation in the spreadsheet and the females would be a second calculation.

1. Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

2. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

3. Find the mean and standard deviation of the DRIVE variable by copying that variable into the Week 1 spreadsheet. Use the Week 4 spreadsheet to determine the percentage of data points from that data set that we would expect to be less than 40. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction?

4. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 40 and 70 as well as for more than 70. Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference?

Monte Carlo Simulation

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

You can use this partial template to guide you:

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Tully Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)

A poll found that 74% of a random sample of 1029 adults said that they believe in ghosts.

determine the margin of error

1.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

86

70

80

76

70

67

y

57

43

46

50

50

41

Given that Se ≈ 4.075, a ≈ 16.319, b ≈ 0.435, and x bar≈ 74.833 , ∑x = 449, ∑y = 287, ∑x2 = 33,861, and ∑y2 = 13,895, find a 99% confidence interval for y when x = 72.

Select one:

a. between 25.3 and 66.8

b. between 25.6 and 66.6

c. between 25.8 and 66.3

d. between 27.0 and 65.1

e. between 24.9 and 67.2

2.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

65

80

68

64

69

71

y

43

49

51

47

42

52

Given that Se ≈ 4.306, a ≈ 17.085, b ≈ 0.417, and x bar≈ 69.5 , ∑x = 417, ∑y = 284, ∑x2 = 29,147, and ∑y2 = 13,528, find a 98% confidence interval for y around 53.4 when x = 87.

Select one:

a. between 26.4 and 77.3

b. between 25.1 and 78.6

c. between 24.6 and 79.1

d. between 21.3 and 82.5

e. between 23.8 and 79.9

3.Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x

81

65

78

87

70

81

y

46

48

54

51

44

51

Given that Se ≈ 3.668, a ≈ 16.331, b ≈ 0.436, and x bar≈ 77 , use a 5% level of significance to find the P-Value for the test that claims β is greater than zero.

Select one:

a. 0.1 <  P-Value < 0.2

b. 0.005 <  P-Value < 0.01

c. P-Value < 0.005

d. 0.2 <  P-Value < 0.25

e. P-Value > 0.25

Park Rangers in a Yellowstone National Park have determined that fawns less than 6 months old have a body weight that is approximately normally distributed with a mean µ = 26.1 kg and standard deviation σ = 4.2 kg. Let x be the weight of a fawn in kilograms. Complete each of the following steps for the word problems below:  Rewrite each of the following word problems into a probability expression, such as P(x>30).  Convert each of the probability expressions involving x into probability expressions involving z, using the information from the scenario.  Sketch a normal curve for each z probability expression with the appropriate probability area shaded.  Solve the problem.

1. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs less than 25 kilograms?

2. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs more than 19 kilograms?

3. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs between 30 and 38 kilograms?

4. If a fawn less than 6 months old weighs 16 pounds, would you say that it is an unusually small animal? Explain and verify your answer mathematically.

5. What is the weight of a fawn less than 6 months old that corresponds with a 20% probability of being randomly selected? Explain and verify your answer mathematically.

1. How long does it take an ambulance to respond to a request for emergency medical aid? One of the goals of one study was to estimate the response time of ambulances using warning lights (Ho & Lindquist, 2001). They timed a total of 67 runs in a small rural county in Minnesota. They calculated the mean response time to be 8.51 minutes, with a standard deviation of 6.64 minutes. Calculate a 95% confidence interval for the mean for this set of data.

1. State the desired level of confidence.
2. Calculate the confidence interval and confidence limits.
   • (1) Calculate the standard error of the mean (s¯¯¯X).(sX¯).
   • (2) Calculate the degrees of freedom (df ) and identify the critical value of t.
   • (3) Calculate the confidence interval and confidence limits.
3. Draw a conclusion about the confidence interval.

a 95% confidence interval was constructed for N = 67 ambulance runs. Assuming the mean and standard deviation remained the same (¯¯¯X=8.51,s=6.64)…(X¯=8.51,s=6.64)…

1. What is the confidence interval for the mean for N = 125 ambulance runs rather than 67?
2. What is the confidence interval for the mean for N = 33 ambulance runs rather than 67?
3. How do these two confidence intervals compare with the 95% confidence interval of (6.89, 10.13) calculated in Exercise 8?

2. For each of the following situations, calculate a 95% confidence interval for the mean (σ known), beginning with the step, “Identify the critical value of z.”

1. ¯¯¯X=50.00,σ¯¯¯X=3.00