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 *n**p* < 10 and *n*(1 −
*p*) < 10. Yes, because *n**p* > 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
displayed, you are strongly encouraged to reload this page after
opening. In order to make sure that all math formatting is properly
displayed, you are strongly encouraged to reload this page after
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

Kay listens to either classical or country music every day while she works. If she listens to classical music one day, there is a 66% chance that she will listen to country music the next day. If she listens to country music, there is a 77% that she will listen to classical music the next day.

(a) If she listens to country music on Monday, what is the probability she will listen to country music on Thursday?

All of the same information about Kay's listening habits remain
true. However, suppose you know the additional fact that on a
**particular** Monday the probability that she is
listening to classical music is 0.24.

(b) Based on your additional knowledge that there is a 0.24
probability that she is listening to classical music on Monday,
what is the probability she will be listening to country music on
Wednesday?

(c) Based on your additional knowledge that there is a 0.24
probability that she is listening to classical music on Monday,
what is the probability that she will be listening to classical
music on Thursday?

In: Math

Every morning Mary randomly decides on one of three possible ways to get to work. She makes her choice so that all three choices are equally likely. The three choices are described as follows: • Choice A (Drives the highway): The highway has no traffic lights but has the possibility of accidents. The number of accidents on the highway for the hour preceding Mary’s trip, X, follows a Poisson distribution with an average of 2. The time (minutes) it takes her to get to work is affected by the number of accidents in the hour preceding her trip due to clean up. The time (in minutes) it takes her is given by T = 54.5 + 5X. • Choice B (Drives through town): Suppose there is no possibility of being slowed down by accidents while going through town. However, going through town she must pass through 10 traffic lights. Suppose all traffic lights act independently from one another and for each there is a probability of 0.5 that she will have to stop and wait (because it is red). Let Y be the number of lights she will stop and wait at. The time (in minutes) it takes her is given by T = 58.5 + Y. • Choice C (Takes the train): Trains arrive for pick-up every 5 minutes. If the train has room, it will take her exactly 50 minutes to get to work. If an arriving train is full she will have to wait an additional 5 minutes until the next train arrives. Trains going through the station will arrive full with probability 0.75, and thus she cannot get on and will have to wait until the next train. Suppose it takes Mary exactly 5 minutes to get to the train station and she always arrives at the station just as a train arrives. Let Z be the number of trains she’ll see until she can finally board (the train isn’t full). The time (in minutes) it takes her is given by T = 50 + 5Z.

a) Which choice should she make every morning to minimize her expected travel time?

b) On one morning Mary starts her journey to work at 7am. Suppose it is necessary that she is at work at or before 8:00 am. Which route should she take to maximize the probability that she is at work at or before 8:00am?

In: Math

5.34 Number of friends on Facebook. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from its Internet Project survey. One was that the average adult user of Facebook has 338 friends. This population distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 200 friends. 8 Suppose that σ = 380 and you take an SRS of 80 adult Facebook users. For your sample, what are the mean and standard deviation of x ¯, the mean number of friends per adult user? Use the central limit theorem to find the probability that the average number of friends for 80 Facebook users is greater than 350.

In: Math