In a poll, 412 of 1030 randomly selected adults aged 18 or older stated that they believe there is too little spending on national defense. Use this information to complete parts (a) through (d) below.

(A) Obtain a point estimate for the proportion of adults aged 18 or older who feel there is too little spending on national defense.

(B) Are the requirements for construction a confidence interval about p satisfied?

-a) Yes, the requirements are satisfied.

-b) No, the requirements of the sample being a random sample are not satisfied.

-c) No, the requirement that np(1-p) is greater than 10 is not satisfied.

-d) No, the requirement that the sample size is no more than 5% of the population is not satisfied.

C) Construct a 90% confidence interval for the proportion of adults aged 18 or older who believe there is too little spending on national defense.

The 90% confidence interval is ( ___ , ___ )

D) Is it possible that more than 45% of adults aged 18 or older believe there is too little spending on national defense? Is it likely?

-a) It is possible, but not likely.

-b) It is not possible.

-c) It is possible and likely.

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4

(a) Use a calculator with mean and standard deviation keys to find x bar and s (in percentages). (For each answer, enter a number. Round your answers to two decimal places.) x bar = x bar = % s = %

(b) Compute a 90% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit %

(c) Compute a 99% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit %

(d) The home run percentages for three professional players are below. Player A, 2.5 Player B, 2.2 Player C, 3.8 Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.

We can say Player A falls close to the average, Player B is above average, and Player C is below average.

We can say Player A falls close to the average, Player B is below average, and Player C is above average.

We can say Player A and Player B fall close to the average, while Player C is above average.

We can say Player A and Player B fall close to the average, while Player C is below average.

(e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.

Yes. According to the central limit theorem, when n ≥ 30, the x bar distribution is approximately normal.

Yes. According to the central limit theorem, when n ≤ 30, the x bar distribution is approximately normal.

No. According to the central limit theorem, when n ≥ 30, the x bar distribution is approximately normal.

No. According to the central limit theorem, when n ≤ 30, the x bar distribution is approximately normal.

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 ?

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

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).

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.

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 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?

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)?

. 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.

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.)

(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.)

(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 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.”)

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?

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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.

describe how the presence of possible outliers might be identified on
histograms
dotplots
stem-and-leaf displays
box-and-whisker plots