Suppose that the body weights of lemmings are normally distributed with a mean of 63.8g and a standard seviation of 12.2g.
(a) What proportions of lemmings weigh more than 90g ?
(b)What proportion of lemmings weigh between 40 and 90 g?
(c)We can say that 99% of lemmings weigh more than ____ g.
(d)In a random sample of 20 lemmings what is the probability that exactly 3 weigh more than 90g ?
In: Math
The mean height of women in a country (ages 20−29) is 64.2 inches. A random sample of 65 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume σ=2.59
In: Math
Problem 3.
The average number of thefts at LeBow is three per month. (a) Estimate the probability, p, that at least six thefts occur at LeBow during December. (What inequality are you using?)
(b) Assume now (for parts (b), (c), and (d)) that you are told that the variance of the number of thefts at LeBow in any one month is 2. Now give an improved estimate of p (using an inequality).
(c) Give a Central Limit Theorem estimate for the probability q that during the next 5 years (12 months per year) there are more than 150 thefts at LeBow.
(d) Use an inequality to get the best bounds you can on the probability q estimated in part (c).
In: Math
A survey on men and women’s shopping behavior collected data
from a sample of 50
men and 50 women. The following data on online shopping spending
every month.
Men Women
148 272
211 176
256 251
309 235
190 145
205 179
203 30
208 135
231 200
125 270
149 174
205 123
195 199
178 195
196 192
198 102
110 110
199 184
181 228
168 316
218 170
222 234
206 163
168 245
239 174
130 126
246 227
149 86
262 96
142 185
174 288
181 154
198 217
147 184
143 154
185 217
200 222
166 175
171 265
133 196
295 172
242 113
299 240
209 235
189 269
173 243
109 131
291 134
208 56
227 164
Treat the men as population 1 and the women as population 2.
Formulate the null and
alternative hypotheses and test whether there is evidence of a
difference in the
variances of monthly online shopping spending between men and
women. Please follow
the hypothesis testing steps in arriving at a decision. You must
show all the calculations
in excel spreadsheet.
In: Math
Exercise 11.55 describes a study conducted by Busseri and colleagues (2009) using a group of pessimists. These researchers asked the same question of a group of optimist: optimist rated their past, present, and projected future satisfaction with their lives. Higher scores on the life satisfaction measure indicate higher satisfaction. The data below reproduce the pattern of means that the researchers observed in self-reported life satisfaction of the sample of optimists for the three time points. Do optimists see a rosy future ahead? Persons 1 2 3 4 5 Past 22 23 25 24 26 Present 25 26 27 28 29 Future 24 27 26 28 29 Perform steps 5 and 6 of hypothesis testing. Be sure to complete the source table when calculating the F ratio for step 5. If appropriate, calculate the Tukey HSD for all possible mean comparison. Find the critical value of q and make a decision regarding the null hypothesis for each of the mean comparison. Calculate the R2 measure of effect size for this ANOVA.
In: Math
In the Northern Hemisphere, dolphins routinely swim in
counterclockwise patterns while sleeping. The table below is the
number of minutes spent swimming in a counterclockwise pattern for
8 Northern dolphins over a period of two hours.
77.7 84.8 79.4 84.0 99.6 93.6 89.4 97.2
a. Calculate the true 95% confidence interval for the average
amount of time that a Northern dolphins spends swimming in a
counterclockwise pattern in a two hour period.
Researchers wanted to see if Southern hemisphere dolphins spent the
same or a different amount of time swimming in a clockwise pattern
while sleeping. The number of minutes spent swimming in a
counterclockwise pattern in a two hour time period for 11 Southern
dolphins is below.
63.4 58.6 73.9 68.8 83.2 71.5 96.4 68.3 76.4 81.4 75
Determine if the two populations are the same or different from
each other using the two sample t-test.
b. Clearly state your null and alternate hypothesis.
c. Show your calculations to calculate the t-statistic
d. Do you reject, or fail to reject, your null hypothesis? Why?
In: Math
To carry the Energy Star Logo, a 25 cubic-foot French-door refrigerator must use no more than 574 kW-h/year (ignore the weird units). If they use significantly more than that, they are removed from the list (which recently happened). A sample of 23 refrrigerators o fac ertain modle is tested by an independent company. They are found to use an average of 596 kW-h/year, with a sample standard deviation of 18.7 kW-h/year.
a) Write the hypotheses being tested.
b) Give a p-value range for this claim. is it significant at the a=.05 level, using that level what do you conclude?
c) Before the government makes a final decision, they will do their own study of the same model, but we want to get the margin of error down to 10 kW-h/year. How many refrigerators should they test, assuming a=.05 and that the standard deviation will be about the same as the first study (18.7 kW-h/years)?
In: Math
. The data is separated into 3 columns – Deep Breathing,
Visualization, Leisurely Walk. This time, the difference scores are
entered directly. Run the ANOVA Test and
If your test indicates that there is a significant difference among
the means, then do Tukey’s HSD test.( The data does show a
differemce among means) Then give the confidence intervals for the
differences of the means using a family confidence level of
95%.
I need help solving the problem below.
In your own words and in terms of the problem, describe which relaxation methods result in means that are significantly different from each other and, for the relaxation methods that differ, tell which one seems to be more effective than the other.
| Deep Breathing | Visualization | Leisurely Walk | |
| 12 | 15 | 9 | |
| 2 | 1 | 2 | |
| 3 | 2 | 2 | |
| 3 | 2 | 5 | |
| 8 | 0 | -6 | |
| 6 | 3 | 1 | |
| 4 | 3 | 2 | |
| 5 | 2 | 9 | |
| 5 | 4 | 8 | |
| 2 | 3 | 7 | |
| 7 | 12 | 19 | |
| 5 | 8 | 24 | |
| 15 | 18 | 0 | |
| 13 | 3 | 5 | |
| 11 | 2 | 12 | |
| 11 | 16 | 21 | |
| 17 | 13 | 2 | |
| 15 | 14 | -1 | |
| 16 | 4 | 2 | |
| 10 | 6 | 2 | |
| 13 | 5 | 8 | |
| 4 | 3 | -4 | |
| 18 | 9 | -5 | |
| 1 | 0 | -3 | |
| 2 | 3 | -5 | |
| 4 | 2 | -11 | |
| 13 | 6 | 8 | |
| 15 | 6 | -2 | |
| 28 | 4 | 6 | |
| 18 | 4 | 14 | |
| 6 | 11 | 6 | |
| 15 | 2 | -4 | |
| 9 | 4 | -5 | |
| 7 | 12 | ||
| 5 | 16 | ||
| 18 | 4 | ||
| 18 | -2 | ||
| -8 | 2 | ||
| -6 | |||
| -1 |
In: Math
An article reported that 7% of married couples in the United States are mixed racially or ethnically. Consider the population consisting of all married couples in the United States.
(a) A random sample of n = 50 couples will be selected from this population and p̂, the proportion of couples that are mixed racially or ethnically, will be computed. What are the mean and standard deviation of the sampling distribution of p̂? (Round your standard deviation to four decimal places.)
| mean | ||
| standard deviation |
(b) Is it reasonable to assume that the sampling distribution of
p̂ is approximately normal for random samples of size
n = 50? Explain.
Yes, because np < 10 and n(1 − p) < 10. Yes, because np > 10 and n(1 − p) > 10. No, because np < 10. No, because np > 10.
(c) Suppose that the sample size is n = 250 rather than
n = 50, as in Part (b). Does the change in sample size
change the mean and standard deviation of the sampling distribution
of p̂? What are the values for the mean and standard
deviation when n = 250? (Round your standard deviation to
four decimal places.)
| mean | ||
| standard deviation |
(d) Is it reasonable to assume that the sampling distribution of
p̂ is approximately normal for random samples of size
n = 250? Explain.
Yes, because np < 10. Yes, because np > 10. No, because np < 10. No, because np > 10.
(e) When n = 250, what is the probability that the
proportion of couples in the sample who are racially or ethnically
mixed will be greater than 0.08? (Round your answer to four decimal
places.)
In: Math
In a study on students’ intention to apply for graduate school, a researcher is interested in the difference between Sociology majors and Justice Studies majors at a large state university. The research hypothesizes that the proportion of sociology majors who intend to apply for graduate schools is higher than that of Justice Studies majors. To test this hypothesis, the research interviews 60 juniors and seniors majoring in sociology and 105 in Justice Studies majors. Of the 60 sociology majors, 35 say that they are considering applying; and of the 105 Justice majors, 40 say that are considering applying. Sociology Justice Studies N1 = 60 N2 = 105 f1 = 35 f2 = 40 Please test the hypothesis stated above (i.e. the proportion of sociology majors who are considering applying for graduate school is higher than the proportion of Justice Studies majors.) (10 points). (Note: this is a hypothetical research situation and none of the statistics presented in the above table is “real.”)
In: Math
The quality control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,200 hours. A random sample of 64 CFLs indicates a sample mean life of 7,250 hours.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,500 hours?
b. Compute the p-value and interpret its meaning.
c. Construct a 95% confidence interval estimate of the population mean life of the CFLs.
d. Compare the results of (a) and (c). What conclusions do you reach?
In: Math
In order to make sure that all math formatting is properly
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opening.
Consider the following statistical studies. Which method of data collection would likely be used to collect data for each study? Explain your selection. What is the population of interest?
Would you take a census or use a sampling? Explain. If you would use a sampling, decide what type of sampling technique you would use. Explain your reasoning.
1. A study of the effect of exercise on relieving depression.
2. A study of the success of graduates of a large university in finding a job within one year of graduation.
3. A study of how often people wash their hands in public restrooms.
In: Math
describe how the presence of possible outliers might
be identified on
histograms
dotplots
stem-and-leaf displays
box-and-whisker plots
In: Math
21. Bob’s local pizza place claims it delivers pizzas in 30 minutes on average. Bob is convinced it’s more than that. He does a hypothesis test and gets a p-value of .001.
a. What does Bob conclude?
b. If Bob made the wrong conclusion what error did he make?
c. What would be the impact of his error?
22. Bob’s local pizza place claims it delivers pizzas in 30 minutes on average. Bob is convinced it’s more than that. He does a hypothesis test and gets a p-value of .10.
a. What does Bob conclude?
b. If Bob made the wrong conclusion what error did he make?
c. What would be the impact of his error?
23. Which type of error is the same as the significance level of a hypothesis test?
a. Type 1 error
b. Type 2 error
c. Both
d. Neither
In: Math
Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use = .05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A n=16, x1=6.82, s1= 0.64 Consultant B= N2=10, X2=6.25, S2=0.75
Compute the value of the test statistic (to 2 decimals).
In: Math