A lab is testing the amount of a certain active chemical compound in a particular drug that has been recently developed. The manufacturer claims that the average amount of the chemical is 110 mg. It is known that the standard deviation in the amount of the chemical is 7 mg.
A random sample of 21 batches of the new drug is tested and found to have a sample mean concentration of 104.5 mg of the active chemical.
a)Calculate the 95% confidence interval for the mean amount of the active chemical in the drug. Give your answers to 2 decimal places.
≤ μ ≤
b)At a significance level α = 0.05, the null hypothesis that the population mean amount of the active chemical in the drug is 110 mg is
In: Statistics and Probability
An entrepreneur examines monthly sales (in $1,000s) for 40 convenience stores in Rhode Island. (You may find it useful to reference the appropriate table: z table or t table)
Excel data
Sales  Sqft 
140  1810 
160  2500 
80  1010 
180  2170 
140  2310 
110  1320 
90  1130 
110  1500 
130  1950 
80  1010 
110  1770 
140  1840 
140  2330 
140  2490 
120  1550 
120  1900 
210  2320 
120  1700 
180  2500 
170  2380 
160  1880 
120  1780 
120  1610 
90  1230 
140  1920 
100  1260 
90  1260 
190  2470 
130  2420 
110  1550 
100  1260 
140  2230 
100  1500 
140  1970 
120  1530 
120  1800 
110  1520 
170  2210 
100  1440 
110  1470 
a. Select the null and the alternative hypotheses in order to test whether average sales differ from $130,000.
H_{0}: μ = 130,000; H_{A}: μ ≠ 130,000
H_{0}: μ ≥ 130,000; H_{A}: μ < 130,000
H_{0}: μ ≤ 130,000; H_{A}: μ > 130,000
b1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
b2. Find the pvalue.
pvalue < 0.01
0.01 ≤ pvalue < 0.02
0.02 ≤ pvalue < 0.05
0.05 ≤ pvalue < 0.10
pvalue ≥ 0.10
c. At α = 0.05 what is your conclusion? Do average sales differ from $130,000?
Reject H_{0}; average sales differ from $130,000.
Reject H_{0}; average sales do not differ from $130,000.
Do not reject H_{0}; average sales differ from $130,000.
Do not reject H_{0}; average sales do not differ from $130,000.
In: Statistics and Probability
AlwaysRain Irrigation, Inc., would like to determine capacity requirements for the next four years. Currently two production lines are in place for making bronze and plastic sprinklers. Three types of sprinklers are available in both bronze and plastic: 90degree nozzle sprinklers, 180degree nozzle sprinklers, and 360degree nozzle sprinklers. Management has forecast demand for the next four years as follows:
YEARLY DEMAND  
1 (IN 000s)  2 (IN 000s)  3 (IN 000s)  4 (IN 000s)  
Plastic 90  31  40  52  53  
Plastic 180  14  16  17  14  
Plastic 360  52  52  63  65  
Bronze 90  6  6  5  15  
Bronze 180  2  2  5  13  
Bronze 360  10  12  11  22  
Both production lines can produce all the different types of
nozzles. The bronze machines needed for the bronze sprinklers
require three operators and can produce up to 18,000 sprinklers.
The plastic injection molding machine needed for the plastic
sprinklers requires four operators and can produce up to 300,000
sprinklers. Three bronze machines and only one injection molding
machine are available.
What are the capacity requirements for the next four years? (Assume that there is no learning.) (Enter the demand values in thousands. Round your answers to 2 decimal places.)
Year 1  Year 2  Year 3  Year 4  
Plastic  
Demand for plastic sprinklers  
Percentage of capacity used  %  %  %  %  
Machine requirements  
Labor requirements  
Bronze  
Demand for bronze sprinklers  
Percentage of capacity used  %  %  %  %  
Machine requirements  
Labor requirements  
In: Statistics and Probability
A manufacturing shop is designed to operate most efficiently at an output of 580 units per day. In the past month the plant averaged 510 units per day.
What was their capacity utilization rate last month? (Round your answer to 1 decimal place.)
Capacity utilization rate %
In: Statistics and Probability
Question text
In a random sample of 200 people, 32 people have blue eyes (characteristic B). Which of the following 95% confidence intervals estimate the true proportion pp of measurements in the population with characteristic B?
Select one:
a. (0.109, 0.211)
c. (0.431, 0.712)
d. (0.561, 0.912)
In: Statistics and Probability
The score of 24 randomly selected exams in a geometry class are given below:
72 85 62 88 75 65 76 99 74 67 83 50 98 78 90 70 80 55 78 77 70 80 68 60
It has been reported that the mean score of all geometry exams is less than 78. Test the validity of the report at α = 0.02 by using the data given above.
(a) Clearly, state H0 and H1, identify the claim and type of test.
H0 :
H1 :
b) Find and name all related critical values, draw the distribution, and clearly mark and shade the critical region(s).
(c) Find the computed test statistic and the Pvalue.
C.T.S. :
PValue :
(d) Use nonstatistical terminology to state your final conclusion about the claim.
It has also been reported that the standard deviation of all scores in a geometry exam is 10. Test the validity of the report at α = 0.01 by using the data given above.
(e) Clearly, state H0 and H1, identify the claim and type of test.
H0 :
H1 :
(f) Find and name all related critical values, draw the distribution, clearly mark and shade the critical region(s).
(g) Find the computed test statistic and the Pvalue.
C.T.S. :
PValue :
(h) Use nonstatistical terminology to state your final conclusion about the claim.
In: Statistics and Probability
The average driving distance (yards) and driving accuracy(percent of drives that land in the fairway) for 8 golfers are recorded in the table to the right. Complete parts a through e below. 
Player 
Distance (yards) 
Accuracy (%) 


1 
316.1316.1 
44.6 

2 
303.3 
51.7 

3 
309.4 
47.5 

4 
311.6 
40.6 

5 
295.3 
55.4 

6 
290.4 
58.9 

7 
295.8 
56.2 

8 
304.3 
49.5 
a. Write the equation of a straightline model relating driving accuracy (y) to driving distance (x). Choose the correct answer below.
A.y =β1x
B.y=β1x2+β0
C.y=β1x+ε
D.y=β0+β1x+ε
Your answer is correct.
b. Fit the model, part
a,to the data using simple linear regression. Give the least squares prediction equation.ModifyingAbove y with caretyequals= 250.3plus+Left parenthesis negative 0.6587 right parenthesis(−0.6587)x
c. Interpret the estimated yintercept of the line.
Choose the correct answer below.
A.Since a drive with 0% accuracy is outside the range of the sample data, the yintercept has no practical interpretation.
B.For each additional yard in distance, the accuracy is estimated to change by the value of the yintercept.
C.For each additional percentage in accuracy, the distance is estimated to change by the value of theyintercept.
D.Since a drive with distance 0 yards is outside the range of the sample data, the yintercept has no practical interpretation.
Your answer is correct.
d. Interpret the estimated slope of the line. Choose the correct answer below.
A.Since a drive with distance 0 yards is outside the range of the sample data, the slope has no practical interpretation.
B.For each additional percentage in accuracy, the distance is estimated to change by the value of the slope.
C.For each additional yard in distance, the accuracy is estimated to change by the value of the slope.
D.Since a drive with 0% accuracy is outside the range of the sample data, the slope has no practical interpretation.
In: Statistics and Probability
Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data: B: Percent for company 2 5 29 8 21 14 13 12 A: Percent for CEO 1 5 21 13 12 18 9 8 Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 1% level of significance. Will you use a left tailed, right tailed, or two tailed test? Select one: a. two tailed test b. right tailed test c. left tailed test
In: Statistics and Probability
The heights of 18yearold men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of twenty 18yearold men will be less than 69 inches? Round your answer to four decimal places.
In: Statistics and Probability
The (simulated) data (mg decrease per decilitre of blood) for the Omega3 group is stored in Table A1, and the data for the control group is stored in Table A2. You are required to calculate a 95% confidence interval for the average difference in cholesterol reduction and to test the hypothesis that there was no difference between the two diets in average reduction of cholesterol.
1. How many patients were in each diet group?
2. What was the mean (decrease) in cholesterol for the Omega3 group of patients?
3. What was the standard deviation in that group? LABORATORY ASSIGNMENTS INTRODUCTORY STATISTICS LABORATORY 37
4. What was the mean (decrease) in cholesterol for the control group of patients?
5. What was the standard deviation in the control group?
6. What is the estimated difference of means?
7. Standard error of the difference between means 2 2 2 1 2 1 n s n s = + What is the standard error of the difference of means?
b) Calculate the margin of error of the estimated difference of means. For this largesample 95% confidence interval we can approximate with a z value which is z0.025 = 1.96. Calculate the confidence interval as difference between means ± margin of error.
8. What is the margin of error of the estimated difference?
9. What is the lower limit for the 95% confidence interval of the difference in cholesterol reduction between Omega3 and control diets?
10. What is the upper limit?
DATA A1:
86.6  
73.9  
99.4  
67.9  
82.3  
80.3  
82.8  
77.9  
76.8  
85.9  
62.5  
34  
120.9  
57  
114.9  
83.7  
103.5  
67.4  
86.1  
87.6  
104.2  
123  
91.7  
95.2  
95.8  
90.7  
72.9  
72.9  
62  
98.1  
70  
77.3  
34.8  
58  
66.7  
100.6  
98.6  
75  
52.9  
54  
42.1  
86.7  
68.9  
68.8  
76  
87.1  
99.2  
119.3  
88.5  
90.9 DATA A2

In: Statistics and Probability
To study how social media may influence the products consumers buy, researchers collected the opening weekend box office revenue (in millions of dollars) for 23 recent movies and the social media message rate (average number of messages referring to the movie per hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue (y) and message rate (x).
Message Rate 
Revenue ($millions) 


1363.2 
146 

1219.2 
79 

681.2 
67 

583.6 
37 

454.7 
35 

413.9 
34 

306.2 
21 

289.8 
18 

245.1 
18 

163.9 
17 

148.9 
16 

147.4 
15 

147.3 
15 

123.6 
14 

118.1 
13 

108.9 
13 

100.1 
12 

90.3 
11 

89.1 
6 

70.1 
6 

56.2 
5 

41.6 
3 

8.4 
1 
The least squares regression equation is ModifyingAbove y with caret=________+ ( _______ )x. (Round to three decimal places as needed.) 

PrintDone
In: Statistics and Probability
1. A population of values has a normal distribution with μ=182.1 and σ=28.9. You intend to draw a random sample of size n=117.
Find the probability that a single randomly selected value is
less than 187.7.
P(X < 187.7) =
Find the probability that a sample of size n=117is randomly
selected with a mean less than 187.7.
P(¯x < 187.7) =
2.
CNNBC recently reported that the mean annual cost of auto insurance
is 1045 dollars. Assume the standard deviation is 211 dollars. You
take a simple random sample of 69 auto insurance policies.
Find the probability that a single randomly selected value is less
than 977 dollars.
P(X < 977) =
Find the probability that a sample of size n=69= is randomly
selected with a mean less than 977 dollars.
P(¯xx¯ < 977) =
In: Statistics and Probability
Very Bad Drugs Corp believes that their new drug, Brain Boost, increases focus and alertness by 15%. Answer the following:
(a)Formulate a set of two hypotheses to test their claim in words and symbols.
(b) What would a Type 1 error be?
(c) What would a Type 2 error be?
In: Statistics and Probability
Q2: Do social recommendations increase ad effectiveness? A study of online viewers who arrived at an advertising video for a particular brand by following a social media recommendation link to viewers who arrived at the same video by web browsing. Data were collected on whether the viewer could correctly recall the brand being advertised after seeing the video. The results were:
Yes No
Recommendation 407 150
Browsing 193 91
Determine whether brand recall is higher following a social media recommendation than with only web browsing at alpha=.05.
1. What is the claim from the question? What are Null and Alternative Hypothesis for this problem?
2. What kind of test do you want to use?
A. Two Samples Independent Population T Test with Equal Variance
B. Two Samples related Population T Test
C. Two Samples Independent Population T Test with Unequal Variance
D. Two Sample Proportion Z Test
E. Two Sample Variance F Test
3. Calculate Test Statistics
4. Find Critical Value(s) and appropriate degree of freedom if necessary Test Statistics:
5. Find Pvalue
6. What is the conclusion that you could make? Clearly write down the conclusion and business statement and illustrate what type error you could make.
In: Statistics and Probability