1)
A report says that 82% of British Columbians over the age of 25 are high school graduates. A survey of randomly selected British Columbians included 1290 who were over the age of 25, and 1135 of them were high school graduates. Does the city’s survey result provide sufficient evidence to contradict the reported value, 82%?
Part i) What is the parameter of
interest?
A. The proportion of all British Columbians (aged
above 25) who are high school graduates.
B. Whether a British Columbian is a high school
graduate.
C. All British Columbians aged above 25.
D. The proportion of 1290 British Columbians (aged
above 25) who are high school graduates.
Part ii) Let pp be the population proportion of
British Columbians aged above 25 who are high school graduates.
What are the null and alternative hypotheses?
A. Null: p=0.88p=0.88. Alternative:
p≠0.88p≠0.88.
B. Null: p=0.82p=0.82. Alternative:
p=0.88p=0.88.
C. Null: p=0.82p=0.82. Alternative:
p>0.82p>0.82.
D. Null: p=0.88p=0.88. Alternative:
p>0.88p>0.88.
E. Null: p=0.82p=0.82. Alternative: p≠0.82p≠0.82
.
F. Null: p=0.88p=0.88. Alternative:
p≠0.82p≠0.82.
Part iii) The PP-value is less than 0.0001.
Using all the information available to you, which of the following
is/are correct? (check all that apply)
A. The reported value 82% must be false.
B. Assuming the reported value 82% is correct, it
is nearly impossible that in a random sample of 1290 British
Columbians aged above 25, 1135 or more are high school
graduates.
C. The observed proportion of British Columbians
who are high school graduates is unusually high if the reported
value 82% is correct.
D. The observed proportion of British Columbians
who are high school graduates is unusually low if the reported
value 82% is correct.
E. The observed proportion of British Columbians
who are high school graduates is unusually high if the reported
value 82% is incorrect.
F. The observed proportion of British Columbians
who are high school graduates is unusually low if the reported
value 82% is incorrect.
G. Assuming the reported value 82% is incorrect,
it is nearly impossible that in a random sample of 1290 British
Columbians aged above 25, 1135 or more are high school
graduates.
Part iv) What is an appropriate conclusion for
the hypothesis test at the 5% significance level?
A. There is sufficient evidence to contradict the
reported value 82%.
B. There is insufficient evidence to contradict
the reported value 82%.
C. There is a 5% probability that the reported
value 82% is true.
D. Both A. and C.
E. Both B. and C.
Part v) Which of the following scenarios
describe the Type II error of the test?
A. The data suggest that reported value is correct
when in fact the value is incorrect.
B. The data suggest that reported value is correct
when in fact the value is correct.
C. The data suggest that reported value is
incorrect when in fact the value is correct.
D. The data suggest that reported value is
incorrect when in fact the value is incorrect.
Part vi) Based on the result of the hypothesis
test, which of the following types of errors are we in a position
of committing?
A. Type I error only.
B. Type II error only.
C. Both Type I and Type II errors.
D. Neither Type I nor Type II errors.
2)
(1 point) McBeans magazine recently published a news article about caffeine consumption in universities that claims that 80% of people at universities drink coffee regularly. Moonbucks, a popular coffee chain, is interested in opening a new store on UBC campus. After reading McBeans' article, they will consider opening a store in UBC if more than 80% of the people in UBC drink coffee regularly. A random sample of people from UBC was taken, and it was found that 680 out of 810 survey participants considered themselves as regular coffee drinkers. Does Moonbucks' survey result provide sufficient evidence to support opening a store at UBC?
Part i) What is the parameter of
interest?
A. Whether a person at UBC drinks coffee
regularly.
B. The proportion of all people at UBC that drink
coffee regularly.
C. The proportion of people at UBC that drink
coffee regularly out of the 810 surveyed.
D. All people at UBC that drinks coffee
regularly.
Part ii) Let pp be the population proportion of
people at UBC that drink coffee regularly. What are the null and
alternative hypotheses?
A. Null: p=0.84p=0.84. Alternative:
p≠0.84p≠0.84.
B. Null: p=0.84p=0.84. Alternative:
p>0.80p>0.80.
C. Null: p=0.80p=0.80. Alternative:
p>0.80p>0.80 .
D. Null: p=0.84p=0.84. Alternative:
p>0.84p>0.84.
E. Null: p=0.80p=0.80. Alternative:
p=0.84p=0.84.
F. Null: p=0.80p=0.80. Alternative:
p≠0.80p≠0.80.
Part iii) The PP-value is found to be about
0.0025. Using all the information available to you, which of the
following is/are correct? (check all that apply)
A. The observed proportion of people at UBC that
drink coffee regularly is unusually low if the reported value 80%
is correct.
B. Assuming the reported value 80% is incorrect,
there is a 0.0025 probability that in a random sample of 810, at
least 680 of the people at UBC regularly drink coffee
C. Assuming the reported value 80% is correct,
there is a 0.0025 probability that in a random sample of 810, at
least 680 of the people at UBC regularly drink coffee.
D. The observed proportion of people at UBC that
drink coffee regularly is unusually low if the reported value 80%
is incorrect.
E. The observed proportion of people at UBC that
drink coffee regularly is unusually high if the reported value 80%
is correct.
F. The observed proportion of people at UBC that
drink coffee regularly is unusually high if the reported value 80%
is incorrect.
G. The reported value 80% must be false.
Part iv) What is an appropriate conclusion for
the hypothesis test at the 5% significance level?
A. There is sufficient evidence to support opening
a store at UBC.
B. There is insufficient evidence to support
opening a store at UBC.
C. There is a 5% probability that the reported
value 80% is true.
D. Both A. and C.
E. Both B. and C.
Part v) Which of the following scenarios
describe the Type II error of the test?
A. The data do not provide sufficient evidence to
support opening a store at UBC when in fact the true proportion of
UBC people who drink coffee regularly exceeds the reported value
80%.
B. The data provide sufficient evidence to support
opening a store at UBC when in fact the true proportion of UBC
people who drink coffee regularly is equal to the reported value
80%.
C. The data provide sufficient evidence to support
opening a store at UBC when in fact the true proportion of UBC
people who drink coffee regularly exceeds the reported value
80%.
D. The data do not provide sufficient evidence to
support opening a store at UBC when in fact the true proportion of
UBC people who drink coffee regularly is equal to the reported
value 80%.
Part vi) Based on the result of the hypothesis
test, which of the following types of errors are we in a position
of committing?
A. Type II error only.
B. Both Type I and Type II errors.
C. Type I error only.
D. Neither Type I nor Type II errors.
3)Suppose some researchers wanted to test the hypothesis that
living in the country is better for your lungs than living in a
city. To eliminate the possible variation due to genetic
differences, suppose they located five pairs of identical twins
with one member of each twin living in the country, the other in a
city. For each person, suppose they measured the percentage of
inhaled tracer particles remaining in the lungs after one hour: the
higher the percentage, the less healthy the lungs. Suppose they
found that for four of the five twin pairs the one living in the
country had healthier lungs.Is the alternative hypothesis one-sided
or two-sided?one-sided
one-sided or two-sided
two-sided
none of these answersHere are the probabilities for the number of
heads in five tosses of a fair coin:
# Heads | 0 | 1 | 2 | 3 | 4 | 5 |
Probability | 0.03125 | 0.15625 | 0.3125 | 0.3125 | 0.15625 | 0.03125 |
Compute the p-value and state your conclusion.p-value = 0.15625
+ 0.03125 = 0.1875 and we have little evidence that individuals
living in the country have healthier lungs than those individuals
living in cities.
p-value = 0.03125 and we have little evidence that individuals
living in the country have healthier lungs than those individuals
living in cities.
p-value = 0.15625 and we have little evidence that individuals
living in the country have healthier lungs than those individuals
living in cities.
p-value = 0.15625 - 0.03125 = 0.125 and we have little evidence
that individuals living in the country have healthier lungs than
those individuals living in cities.
In: Math
An elevator has a placard stating that the maximum capacity is 2520 lblong dash15 passengers. So, 15 adult male passengers can have a mean weight of up to 2520 divided by 15 equals 168 pounds. If the elevator is loaded with 15 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 168 lb. (Assume that weights of males are normally distributed with a mean of 175 lb and a standard deviation of 31 lb.) Does this elevator appear to be safe?
The probability the elevator is overloaded is?
Does this elevator appear to be safe?
In: Math
The frequency distribution shows the average seasonal rainfall in California measured in inches
Please complete the chart (frequency and cumulative relative frequency) CRF to two decimal points
Rainfall Frequency Cumulative Relative Frequency
0 -9.99 2
10 – 19.99 25
20 - 29.99 0.88
30 -30.99 0.98
40 – 40.99 1.00
Total 50
I would like a clear understanding of where the values come from to complete this chart. I have seen a couple of answers that do not clearly explain how the missing values are generated (Formulas).
In: Math
Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players: x_{1}; n_{1} = 21
248 | 263 | 254 | 251 | 244 | 276 | 240 | 265 | 257 | 252 | 282 |
256 | 250 | 264 | 270 | 275 | 245 | 275 | 253 | 265 | 270 |
Weights (in lb) of pro basketball players: x_{2}; n_{2} = 19
202 | 200 | 220 | 210 | 193 | 215 | 222 | 216 | 228 | 207 |
225 | 208 | 195 | 191 | 207 | 196 | 182 | 193 | 201 |
(a) Use a calculator with mean and standard deviation keys to calculate x_{1}, s_{1}, x_{2}, and s_{2}. (Round your answers to one decimal place.)
x_{1} = | |
s_{1} = | |
x_{2} = | |
s_{2} = |
(b) Let μ_{1} be the population mean for
x_{1} and let μ_{2} be the
population mean for x_{2}. Find a 99% confidence
interval for μ_{1} − μ_{2}.
(Round your answers to one decimal place.)
lower limit | |
upper limit |
In: Math
Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of μ = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 39 waves showed an average wave height of x = 17.2 feet. Previous studies of severe storms indicate that σ = 3.8 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to two decimal places.) test statistic = critical value = State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the average storm level is increasing. Reject the null hypothesis, there is insufficient evidence that the average storm level is increasing. Fail to reject the null hypothesis, there is sufficient evidence that the average storm level is increasing. Fail to reject the null hypothesis, there is insufficient evidence that the average storm level is increasing. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? The conclusions obtained by using both methods are the same. We reject the null hypothesis using the traditional method, but fail to reject using the P-value method. We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.
In: Math
Consider the following time series data:
Month 1 2 3 4 5 6 7
Value 25 14 19 11 18 22 16
(a) Compute MSE using the most recent value as the forecast for the next period. If required, round your answer to one decimal place. What is the forecast for month 8? If required, round your answer to one decimal place. Do not round intermediate calculation.
(b) Compute MSE using the average of all the data available as the forecast for the next period. If required, round your answer to one decimal place. Do not round intermediate calculation. What is the forecast for month 8? If required, round your answer to one decimal place.
In: Math
Going back to problem 1, in real life you can, without much difficulty, get the mean grades of Prof. Lax’s classes but that is about it; meaning you will have no idea how his grades would be distributed, nor would you have any idea about the standard deviation of these grades. (I doubt Prof. Lax would advertise his laxness on his website. Contrary what you might believe that is academically bad form and might negatively affect his students’ hireability in the job market). However, you have access to Miss Z’s data (which she swears is obtained by a random selection process) and the grades she obtained in her random sample of nine were:
79, 75, 84, 63, 98, 52, 87, 99, 83
a .to help Miss Z with her decision to take this course with Prof. Lax or not, create a 97% confidence interval (CI) for the mean using Miss Z.’s data. Make sure that you do the necessary checks.
b. Does your interval capture the rumored population mean of 85?
c. Calculate the margin of error (ME or simply E) of your confidence interval.
d. Miss Z thinks a margin of error (or E) of 7 points or more will have a significant negative effect on her GPA. How does the ME (or E) of your 97% CI from part (c) compare to what she says her GPA can afford? If your CI’s ME (or E) is different than 7 points she can afford what are the ways you can use to reduce the margin of error down to 7 or smaller. Discuss all that can be done. 3
In: Math
When evaluating research, what factors should be considered? Why are these factors important? Provide some examples to illustrate the importance of each factor.
In: Math
The lengths of a particular animal's pregnancies are approximately normally distributed, with mean mu equals280 days and standard deviation sigma equals12 days. (a) What proportion of pregnancies lasts more than 295 days? (b) What proportion of pregnancies lasts between 259 and 283 days? (c) What is the probability that a randomly selected pregnancy lasts no more than 262 days? (d) A "very preterm" baby is one whose gestation period is less than 250 days. Are very preterm babies unusual?
In: Math
For each of the following cases, assume a sample of n observations is taken from a normally distributed population with unknown mean μ and unknown variance σ2. Complete the following: i) Give the form of the test statistic. ii) State and sketch the shape of the prob. distribution of the test statistic when the null hypothesis is true. iii) Give the range of values of the test statistic which comprises the rejection region. iv) Sketch in the area(s) associated with α on the probability distribution of the test statistic. v) Compute the observed value of the test statistic. Give the approximate size of the p-value. vi) Using the observed value of the test statistic, state your conclusions with the appropriate probability statement. a. H0: σ2< 15; HA: σ2> 15, α = .05, n = 50, s2= 19.5
b. H0: σ2= 20 ; HA: σ2≠20, α = .05, n = 50, s2= 22.1
In: Math
Exam grades across all sections of introductory statistics at a large university are approximately normally distributed with a mean of 72 and a standard deviation of 11. Use the normal distribution to answer the following questions.
(a) What percent of students scored above an 88 ?Round your answer to one decimal place.
(b) What percent of students scored below a 59 ?Round your
answer to one decimal place.
(c) If the lowest 7%of students will be required to attend peer
tutoring sessions, what grade is the cutoff for being required to
attend these sessions?Round your answer to one decimal place.
(d) If the highest 9%of students will be given a grade of A,
what is the cutoff to get an A? Round your answer to one decimal
place.
In: Math
What is factor analysis? in which situation is it useful?
In: Math
Retaking the SAT (Raw Data, Software Required): Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. The Senior year scores (x) and associated Junior year scores (y) are given in the table below. This came from a random sample of 35 students. Use this data to test the claim that retaking the SAT increases the score on average by more than 27 points. Test this claim at the 0.01 significance level. (a) The claim is that the mean difference (x - y) is greater than 27 (μd > 27). What type of test is this? This is a left-tailed test. This is a two-tailed test. This is a right-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. t d = (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0 (e) Choose the appropriate concluding statement. The data supports the claim that retaking the SAT increases the score on average by more than 27 points. There is not enough data to support the claim that retaking the SAT increases the score on average by more than 27 points. We reject the claim that retaking the SAT increases the score on average by more than 27 points. We have proven that retaking the SAT increases the score on average by more than 27 points. Senior Score (x) Junior Score (y) (x - y) 1093 1063 30 1238 1195 43 1238 1186 52 1112 1099 13 1289 1248 41 1109 1098 11 1061 1055 6 1102 1056 46 1139 1087 52 1090 1076 14 1157 1118 39 1263 1223 40 1279 1240 39 1117 1086 31 1226 1191 35 1216 1187 29 1324 1268 56 1199 1173 26 1279 1244 35 1165 1128 37 1151 1124 27 1159 1124 35 1256 1224 32 1255 1231 24 1129 1093 36 1299 1270 29 1261 1207 54 1207 1187 20 1156 1147 9 1177 1150 27 1253 1234 19 1320 1274 46 1200 1122 78 1234 1213 21 1143 1143 0
In: Math
Q 15 Question 15 Consider the following sample of 11 length-of-stay values (measured in days): 1, 1, 3, 3, 3, 4, 4, 4, 4, 5, 7 Now suppose that due to new technology you are able to reduce the length of stay at your hospital to a fraction 0.5 of the original values. Thus, your new sample is given by .5, .5, 1.5, 1.5, 1.5, 2, 2, 2, 2, 2.5, 3.5 Given that the standard error in the original sample was 0.5, in the new sample the standard error of the mean is _._. (Truncate after the first decimal.)
In: Math
Question 2: The efficacies of two drugs, X and Y were evaluated in two groups of mice (Group C, Group D). The outcome was the concentration of the drug in the plasma after giving the mice drugs (through drinking water) for 24 hours. The data were summarized below.
Group C |
Group D |
3 |
10 |
4 |
7 |
6 |
11 |
6 |
10 |
7 |
9 |
5 |
11 |
6 |
12 |
5 |
14 |
8 |
8 |
9 |
13 |
Question 2A. At the significance level of 0.05, are the drug concentrations in Group C and Group D different? Using Mann-Whitney U test here.
In: Math