Here are summary statistics for randomly selected weights of newborn girls:
nequals=221
x overbar x=28.8
hg,
s=7.9
hg. Construct a confidence interval estimate of the mean. Use a
99%
confidence level. Are these results very different from the confidence interval
25.0
hg less than<muμless than<31.4
hg with only
12
sample values,
x overbarxequals=28.2
hg, and
sequals=3.6
hg?
What is the confidence interval for the population mean
muμ?
nothing
hgless than<muμless than<nothing
hg (Round to one decimal place as needed.)
Are the results between the two confidence intervals very different?
A.
No, because the confidence interval limits are similar.
B.
Yes, because the confidence interval limits are not similar.
C.
No, because each confidence interval contains the mean of the other confidence interval.
D.
Yes, because one confidence interval does not contain the mean of the other confidence interval.
In: Math
For the remaining models, set up and solve LP models in EXCEL. 4) Optimized Cookie Production for a BCS Party. A friend was bringing small bags of cookies to sell at a fairly large BCS Championship Game Watch Party (there were no TCU fans present, however). Three kinds of cookies were sold: Stars (sold for $1 per bag), Circles (sold for $0.75 per bag), and Stars and Stripes (sold for $1.50 per bag). He was to bring the cookies to the Watch Party in three large boxes. (The boxes did not have to be full, but he could not bring more than three large boxes of cookies). By volume, it is a known fact that one of the large boxes can hold 100 bags of Stars, 120 bags of Circles, or 80 bags of Stars and Stripes (or a corresponding mix of cookies). HINT: Don’t concern yourself with what each box held; view this as an aggregate limit in the numbers of cookies. Previous parties had given him some hints on the demand for cookies – he knew that for the sake of variety, he needed to make at least 45 bags of each type of cookie. As he was planning his cookie composition, he also realized he was constrained by time in putting together the cookie bags. Circle cookies and Stars cookies took 1 minute per bag to finish; because Stars and Stripes had more icing, it took 2 minutes to finish each bag. He allocated 420 minutes (7 hours) to put the bags together. Can you determine how many of each of the three cookie types your friend should make to maximize sales (a surrogate for profit)? To quote POTUS: “Yes, you can!”
•Practice problem #4 out of Module 6. Solve using the Solver in EXCEL.
•There is one modification (Circles in box size) and the following clarification.
•
•2nd paragraph – consider that there are 3 boxes and that you don’t have to fill up the boxes (but you cannot exceed that space).
Each bag of Stars takes up 0.01 (1/100th) of a box
Each bag of Circles takes up 0.008 (1/125th) of a box
Each bag of Stars/Stripes takes up 0.0125 (1/80th) of a box
Use this information to help you in creating the LP Model.
In: Math
1. The effectiveness of a blood-pressure drug is being
investigated. An experimenter finds that, on average, the reduction
in systolic blood pressure is 44 for a sample of size 22 and
standard deviation 6. Estimate how much the drug will lower a
typical patient's systolic blood pressure (using a 95% confidence
level).
Give your answers to one decimal place and provide the point
estimate with its margin of error. __________________ ±
________________________
2. In a survey, 31 people were asked how much they spent on
their child's last birthday gift. The results were roughly
bell-shaped with a mean of $42 and standard deviation of $10.
Estimate how much a typical parent would spend on their child's
birthday gift (use a 95% confidence level).
Give your answers to one decimal place. Provide the point estimate
and margin or error. _______________ ± _________________
3. You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:
| 13.8 |
| 65.2 |
| 51.2 |
| 22.5 |
| 41.7 |
| 13.8 |
| 58.4 |
| 39.4 |
| 32.2 |
| 31.1 |
Find the 80% confidence interval. Enter your answer as an
open-interval (i.e., parentheses)
accurate to two decimal places (because the sample data are
reported accurate to one decimal place). 80% C.I. =
___________________
Answer should be obtained without any preliminary rounding.
4. The effectiveness of a blood-pressure drug is being
investigated. An experimenter finds that, on average, the reduction
in systolic blood pressure is 38.9 for a sample of size 339 and
standard deviation 13.4. Estimate how much the drug will lower a
typical patient's systolic blood pressure (using a 80% confidence
level).
Enter your answer as a tri-linear inequality accurate to one
decimal place (because the sample statistics are reported accurate
to one decimal place).
_________< μ < __________
5. Assume that a sample is used to estimate a population mean
μμ. Find the margin of error M.E. that corresponds to a
sample of size 7 with a mean of 52.6 and a standard deviation of
14.3 at a confidence level of 99.9%. Report ME accurate to one
decimal place because the sample statistics are presented with this
accuracy.
M.E. = ________________ Answer should be
obtained without any preliminary rounding. However, the critical
value may be rounded to 3 decimal places.
6. Express the confidence interval (337.6,540.6)(337.6,540.6) in
the form of ¯x ± ME.
¯x ± ME= ___________ + ______________
7. Assume that a sample is used to estimate a population mean
μμ. Find the 95% confidence interval for a sample of size 66 with a
mean of 27.9 and a standard deviation of 20.8. Enter your answer as
an open-interval (i.e., parentheses)
accurate to one decimal place (because the sample statistics are
reported accurate to one decimal place).
95% C.I. = _____________
Answer should be obtained without any preliminary rounding.
However, the critical value may be rounded to 3 decimal places.
8. Assume that a sample is used to estimate a population
proportion μμ. Find the margin of error M.E. that
corresponds to a sample of size 411 with a mean of 20.9 and a
standard deviation of 20.6 at a confidence level of 90%.
Report ME accurate to one decimal place because the sample
statistics are presented with this accuracy.
M.E. =__________________
Answer should be obtained without any preliminary rounding.
However, the critical value may be rounded to 3 decimal places.
9. In a survey, 16 people were asked how much they spent on
their child's last birthday gift. The results were roughly
bell-shaped with a mean of $38 and standard deviation of $7.
Estimate how much a typical parent would spend on their child's
birthday gift (use a 95% confidence level).
Give your answers to one decimal place. Provide the point estimate
and margin or error. _____________ ± _______________
10. Assume that a sample is used to estimate a population mean
μμ. Find the 90% confidence interval for a sample of size 56 with a
mean of 59.2 and a standard deviation of 13.2. Enter your answer as
an open-interval (i.e., parentheses)
accurate to one decimal place (because the sample statistics are
reported accurate to one decimal place).
90% C.I. = _________________
Answer should be obtained without any preliminary rounding.
However, the critical value may be rounded to 3 decimal places.
11. Assume that a sample is used to estimate a population mean
μμ. Find the margin of error M.E. that corresponds to a
sample of size 21 with a mean of 58.7 and a standard deviation of
17.9 at a confidence level of 80%.
Report ME accurate to one decimal place because the sample
statistics are presented with this accuracy.
M.E. = _______________
Answer should be obtained without any preliminary rounding.
However, the critical value may be rounded to 3 decimal places.
12. Express the confidence interval (174.8,273.6) in the form of ¯x ± ME.
¯x ± ME=_________________
13. Assume that a sample is used to estimate a population
proportion μμ. Find the margin of error M.E. that
corresponds to a sample of size 45 with a mean of 15.3 and a
standard deviation of 6.6 at a confidence level of 99%.
Report ME accurate to one decimal place because the sample
statistics are presented with this accuracy.
M.E. = ________________
Answer should be obtained without any preliminary rounding.
However, the critical value may be rounded to 3 decimal places.
14. You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:
| 32.1 |
| 30.7 |
| 9 |
| 22.2 |
| 42.7 |
| -5.8 |
| 20.5 |
| 20.8 |
| 52.4 |
| 28.6 |
| 9.2 |
Find the 90% confidence interval. Enter your answer as an
open-interval (i.e., parentheses)
accurate to two decimal places (because the sample data are
reported accurate to one decimal place).
90% C.I. = _________________
15. The effectiveness of a blood-pressure drug is being
investigated. An experimenter finds that, on average, the reduction
in systolic blood pressure is 30.9 for a sample of size 889 and
standard deviation 11.3. Estimate how much the drug will lower a
typical patient's systolic blood pressure (using a 95% confidence
level).
Enter your answer as a tri-linear inequality accurate to one
decimal place (because the sample statistics are reported accurate
to one decimal place).
___________< μ < ____________________
16. You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:
| 74.2 |
| 89.8 |
| 70.1 |
| 81.7 |
| 63.6 |
| 94.8 |
| 75.3 |
| 73.3 |
| 76 |
| 66.3 |
| 63 |
Find the 80% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 80% C.I. = _____________________
17. The effectiveness of a blood-pressure drug is being
investigated. An experimenter finds that, on average, the reduction
in systolic blood pressure is 50 for a sample of size 19 and
standard deviation 8. Estimate how much the drug will lower a
typical patient's systolic blood pressure (using a 90% confidence
level).
Give your answers to one decimal place and provide the point
estimate with its margin of error.
______________ ± _______________
In: Math
What is the purpose of hypothesis testing? Do you see any relevance to hypothesis testing in your daily life? This could be school life, personal life, or work life. Start with work life and give us a description of 2–3 scenarios where hypothesis testing may be beneficial for decision-making.
In: Math
Fixed acidity - Volatile acidity - Citric acid - Residual sugar -Chlorides
7.4 0.7 0 1.9 0.076
7.8 0.88 0 2.6 0.098
7.8 0.76 0.04 2.3 0.092
11.2 0.28 0.56 1.9 0.075
7.4 0.7 0 1.9 0.076
7.4 0.66 0 1.8 0.075
7.9 0.6 0.06 1.6 0.069
7.3 0.65 0 1.2 0.065
7.8 0.58 0.02 2 0.073
7.5 0.5 0.36 6.1 0.071
6.7 0.58 0.08 1.8 0.097
7.5 0.5 0.36 6.1 0.071
5.6 0.615 0 1.6 0.089
7.8 0.61 0.29 1.6 0.114
8.9 0.62 0.18 3.8 0.176
8.9 0.62 0.19 3.9 0.17
8.5 0.28 0.56 1.8 0.092
8.1 0.56 0.28 1.7 0.368
7.4 0.59 0.08 4.4 0.086
7.9 0.32 0.51 1.8 0.341
8.9 0.22 0.48 1.8 0.077
7.6 0.39 0.31 2.3 0.082
7.9 0.43 0.21 1.6 0.106
8.5 0.49 0.11 2.3 0.084
6.9 0.4 0.14 2.4 0.085
6.3 0.39 0.16 1.4 0.08
1. For the data on 26 red wines given above, conduct the following analysis:
i. Provide five-number summary i.e. the minimum, 1st quartile, median, 3rd quartile, and maximum value for fixed acidity. Arrange them in increasing order on a straight line, draw a box plot and interpret what it means.
ii. Calculate the correlation coefficient between fixed acidity and volatile acidity and between residual sugar and chlorides. Comment on the strength and direction of association for the two variable pairs.
iii. What can be stated about the cause-effect relationship between fixed acidity and volatile acidity, based on the correlation coefficient score?
In: Math
(22 pts) Find the experimental probability of rolling each sum. Fill out the following table:
|
Sum of the dice |
Number of times each sum occurred |
Probability of occurrence for each sum out of your 108 total rolls (record your probabilities to threedecimal places) |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 | ||
| 10 | ||
| 11 |
In: Math
Mensa is a high IQ society that admits people as members if they can score at the 98th percentile or above on certain standardized IQ (intelligence quotient) tests. On one such test, the Stanford Binet, the qualifying score is 132. The test consists of n questions, each with m choices.
a) On any given test question, the person taking the test knows the answer with probability p. Assume that when the person does not know the answer, the person guesses an option completely at random. Calculate the probability a person knew the answer to a question, given that they answered it correctly.
b) If a person receives a score of 132 or higher on the test, they are considered to have an IQ of 132 or higher. However, individuals with IQ less than 132 can also receive such scores about 0.1% of the time due to lucky guessing. Given that a person is labeled as having IQ of 132 or higher, what is the probability they actually have IQ below 132? Assume that all individuals with IQ of 132 or higher receive an accurate score 95% of the time.
In: Math
A genetic test is used to determine if people have a predisposition for thrombosis, which is the formation of a blood clot inside a blood vessel that obstructs the flow of blood through the circulatory system. It is believed that 3% of people have this predisposition. The test is 95% accurate for those who have the predisposition, and 97% accurate for those who do not have the predisposition.
Simulate the results for administering this test to a population of 100,000 individuals.
a) How many individuals in this hypothetical population are expected to test positive for the predisposition?
b) Estimate the probability that an individual who tests positive has the predisposition.
c) Suppose that two new tests have been developed. Test A improves accuracy for those who have the predisposition to 98% (while accuracy for those who do not have the predisposition remains at 97%), while Test B improves accuracy for those who do not have the predisposition to 99% (while accuracy for those who do have the predisposition remains at 95%).
Which test offers a higher increase in the probability that a person who tests positive actually has the predisposition? Explain the reasoning behind your answer. Limit your answer to at most seven sentences.
In: Math
Assuming IQ scores are normally distributed in the population with a mean of 100 and a standard deviation of 16, what percentages of IQ scores are less than 120, between 110 and 130, and what IQ will place you in the top 8% of the population?
In: Math
An interpersonally Reactivity Scale was give to a POPULATION of juvenile offenders to measure their levels of empathy for victims. Assume scores are NORMALLY DISTRIBUTED with a MEAN = 7.66 and a STANDARD DEVIATION = 1.75.
a. What is the probability of someone scoring a 9.02 of higher?
b. 50% of offenders clustered around the mean would score between what and what?
c. 95% of the offenders clustered around the mean would score between what and what?
In: Math
Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.35, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.45 pound of beef, 0.45 cup of onions, and 5 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.45 pound of beef, 0.72 cup of onions, 1 ounces of Kilgore's special sauce, and 4 ounces of hot sauce. Today, Kilgore has 33 pounds of beef, 47 cups of onions, 81 ounces of Kilgore's special sauce, and 48 ounces of hot sauce on hand.
Let
W = # of servings of Wimpy to make
D = # of servings of Dial 911 to make
| Max | 0.35W | + | 0.59D | |||
| s.t. | ||||||
| 0.45W | + | 0.45D | ≤ | 33 (Beef) | ||
| 0.45W | + | 0.72D | ≤ | 47 (Onions) | ||
| 5W | + | 1D | ≤ | 81 (Special Sauce) | ||
| 4D | ≤ | 48 (Hot Sauce) | ||||
| W, D | ≥ | 0 |
b. Find an optimal solution. Truncate your answers to whole
servings available for sale.
Solution:
W = 13
D = 12
What is the optimal profit? Round your answer to the nearest cent.
Profit = $ __________
In: Math
Use your reading handout to calculate all the necessary parts of a t-test. Use an alpha=0.25 in the t-table to find your critical value.
Population A Population B
(South-East Asia, Migratory) (Australasia, Non-migratory)
Wing length (cm) Wing length (cm)
31 47
50 41
30 41
31 37
42 30
37 34
50 35
45 31
41 33
50 31
45 37
31 47
48 44
39 33 47 35
48 37
50
47
46
39
42
46
In: Math
1.Historical records show that the average per capita consumption of eggs in the US is 278 (this is per year). Lately, consumers have been getting conflicting advice about the benefits and dangers of eggs, and a rural agricultural association wants to know if the average egg consumption has changed. A sample of 50 adults yielded a sample mean egg consumption of 287 eggs and a sample standard deviation of 28 eggs. Construct a null and alternate hypothesis that the association can use to answer their question. Based on the sample data and a 5% level of significance, what can they conclude?
2. In 2010, the average weight of cell phone batteries was 110 grams. Battery technology has continued to improve and a consumer group wants to know if the average weight of cell phone batteries has reduced. A sample of 49 cell phone batteries yielded a sample mean of 108 grams. Historical data shows that the population standard deviation is 10 grams. At the 5% level of significance, can the consumer group conclude that batteries have become lighter? Would your answer change at a 1% level of significance? Justify.
In: Math
Use the data to assess the correlation between hours studying per week in High School and SAT score. Interpret the result and give the conclusion.
| High School hours per week | SAT Score |
| 15 | 1500 |
| 10 | 1250 |
| 2 | 850 |
| 11 | 1350 |
| 0 | 780 |
| 5 | 810 |
| 6 | 900 |
| 10 | 1100 |
| 16 | 1450 |
| 2 | 810 |
In: Math
In an effort to promote a new product, a marketing firm asks participants to rate the effectiveness of ads that varied by length (short, long) and by type of technology (static, dynamic, interactive). Higher ratings indicated greater effectiveness.
| Source of Variation | SS | df | MS | F |
|---|---|---|---|---|
| Length | 5 | |||
| Technology | ||||
| Length × Technology | 142 | |||
| Error | 570 | 114 | ||
| Total | 847 |
(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Assume experimentwise alpha equal to 0.05.)
|
Source of Variation |
SS | df | MS | F |
|---|---|---|---|---|
| Length | 5 | |||
| Technology | ||||
| Length
× Technology |
142 | |||
| Error | 570 | 114 | ||
| Total | 847 |
State the decision for the main effect of length.
Retain the null hypothesis.Reject the null hypothesis.
State the decision for the main effect of technology.
Retain the null hypothesis.Reject the null hypothesis.
State the decision for the interaction effect.
Retain the null hypothesis.Reject the null hypothesis.
(b) Based on the results you obtained, what is the next step?
No further analysis is needed, because none of the effects are significant.Compute pairwise comparisons for the technology factor. Compute simple main effect tests for the significant interaction.Compute pairwise comparisons for the length factor.
In: Math